int

明确和无限的积分GydF4y2Ba

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句法GydF4y2Ba

F=int(expr)

F=int(expr,var)

F=int(expr,a,b)

f = int（expr，var，a，b）GydF4y2Ba

F=int(___GydF4y2Ba那名称，价值）GydF4y2Ba

Description

例GydF4y2Ba

FGydF4y2Ba=int(E.Xpr）GydF4y2Ba计算无限积分的GydF4y2BaE.Xpr。GydF4y2Baint使用默认的集成变量确定GydF4y2BaSymvar.GydF4y2Ba（GydF4y2Baexpr，1GydF4y2Ba）。如果GydF4y2BaE.Xpr是一个常量，那么默认的集成变量是GydF4y2BaXGydF4y2Ba。GydF4y2Ba

例GydF4y2Ba

FGydF4y2Ba=int(E.Xpr那GydF4y2Bavar）GydF4y2Ba计算无限积分的GydF4y2BaE.Xprwith respect to the symbolic scalar variablevar。GydF4y2Ba

例GydF4y2Ba

FGydF4y2Ba=int(E.Xpr那GydF4y2Ba一种GydF4y2Ba那GydF4y2BaB.GydF4y2Ba）GydF4y2Ba计算明确的积分GydF4y2BaE.XprFrom一种GydF4y2BaT.oB.GydF4y2Ba。GydF4y2Baint使用默认的集成变量确定GydF4y2BaSymvar.GydF4y2Ba（GydF4y2Baexpr，1GydF4y2Ba）。如果GydF4y2BaE.Xpr是一个常量，那么默认的集成变量是GydF4y2BaXGydF4y2Ba。GydF4y2Ba

int(expr,[a b])相当于GydF4y2Baint(expr,a,b)。GydF4y2Ba

例GydF4y2Ba

FGydF4y2Ba=int(E.Xpr那GydF4y2Bavar那GydF4y2Ba一种GydF4y2Ba那GydF4y2BaB.GydF4y2Ba）GydF4y2Ba计算明确的积分GydF4y2BaE.Xprwith respect to the symbolic scalar variablevarFrom一种GydF4y2BaT.oB.GydF4y2Ba。GydF4y2Ba

int(expr,var,[a b])相当于GydF4y2Baint（expr，var，a，b）GydF4y2Ba。GydF4y2Ba

例GydF4y2Ba

FGydF4y2Ba=int(___GydF4y2Ba那GydF4y2Ba名称，价值GydF4y2Ba）GydF4y2Baspecifies additional options using one or more名称，价值GydF4y2Ba对论点。例如，GydF4y2Ba'Ignoreanalyticonstraints'那T.rue指定GydF4y2Baint对整体应用额外的简化。GydF4y2Ba

Examples

全部收缩GydF4y2Ba

无限制的单变量表达的积分GydF4y2Ba

Open Live Script

定义一个单变量表达式。GydF4y2Ba

symsXGydF4y2Baexpr = -2 * x /（1 + x ^ 2）^ 2;GydF4y2Ba

Find the indefinite integral of the univariate expression.

F=int(expr)

F=GydF4y2Ba
                      
                        $\frac{1GydF4y2Ba}{{XGydF4y2Ba}^{2GydF4y2Ba} +GydF4y2Ba 1GydF4y2Ba}$

多元函数的无限积分GydF4y2Ba

Open Live Script

使用变量定义多变量函数GydF4y2BaXGydF4y2Ba一种ndZ.GydF4y2Ba。GydF4y2Ba

symsXGydF4y2BaZ.GydF4y2BaF（X那Z.）=X/（1+Z.^2);

Find the indefinite integrals of the multivariate expression with respect to the variablesXGydF4y2Ba一种ndZ.GydF4y2Ba。GydF4y2Ba

FX=int(f,x)

FX（X那Z.）=GydF4y2Ba
                      
                        $\frac{{XGydF4y2Ba}^{2GydF4y2Ba}}{2GydF4y2Ba ({Z.GydF4y2Ba}^{2GydF4y2Ba} +GydF4y2Ba 1GydF4y2Ba)}$

fz = int（f，z）GydF4y2Ba

FZ.（X那Z.）=GydF4y2Ba
                       $XGydF4y2Ba 一种T.一种n （GydF4y2Ba Z.GydF4y2Ba ）GydF4y2Ba$

如果未指定集成变量，则GydF4y2Baint使用返回的第一个变量GydF4y2BaSymvar.GydF4y2Ba如T.he integration variable.

var = symvar（f，1）GydF4y2Ba

var =
                       $XGydF4y2Ba$

F=int(f)

f（x，z）=GydF4y2Ba
                      
                        $\frac{{XGydF4y2Ba}^{2GydF4y2Ba}}{2GydF4y2Ba ({Z.GydF4y2Ba}^{2GydF4y2Ba} +GydF4y2Ba 1GydF4y2Ba)}$

Definite Integrals of Symbolic Expressions

Open Live Script

集成符号表达式GydF4y2Ba0.GydF4y2BaT.o1GydF4y2Ba。GydF4y2Ba

symsXGydF4y2BaE.Xpr = x*log(1+x); F = int(expr,[0 1])

F=GydF4y2Ba
                      
                        $\frac{1GydF4y2Ba}{4.GydF4y2Ba}$

Integrate another expression from罪（T.）GydF4y2BaT.o1GydF4y2Ba。GydF4y2Ba

symsT.GydF4y2BaF=int(2*x,[sin(t) 1])

F=GydF4y2Ba
                       ${COS.GydF4y2Ba （GydF4y2Ba T.GydF4y2Ba ）GydF4y2Ba}^{2GydF4y2Ba}$

W.henintC一种nnot compute the value of a definite integral, numerically approximate the integral by usingVPA.GydF4y2Ba。GydF4y2Ba

symsXGydF4y2BaF=COS.（X）/sqrt(1 + x^2); Fint = int(f,x,[0 10])

Fint =
                      
                        $\int_{0.GydF4y2Ba}^{10.GydF4y2Ba} \frac{COS.GydF4y2Ba （GydF4y2Ba XGydF4y2Ba ）GydF4y2Ba}{\sqrt{{XGydF4y2Ba}^{2GydF4y2Ba} +GydF4y2Ba 1GydF4y2Ba}} D.GydF4y2Ba XGydF4y2Ba$

FVPA =VPA.（Fint)

FVPA =GydF4y2Ba
                       $0.37570628299079723478493405557162GydF4y2Ba$

直接近似积分，使用GydF4y2BaVPA.integral代替GydF4y2BaVPA.GydF4y2Ba。TheVPA.integralFunction is faster and provides control over integration tolerances.

FVPA.int = vpaintegral(f,x,[0 10])

FVPA.int =
                       $0.。375706$

矩阵元素的积分GydF4y2Ba

Open Live Script

定义包含四个表达式的符号矩阵作为其元素。GydF4y2Ba

syms一种GydF4y2BaXGydF4y2BaT.GydF4y2BaZ.GydF4y2Bam = [exp（t）exp（a * t）;sin（t）cos（t）]GydF4y2Ba

m =GydF4y2Ba
                      
                        $（GydF4y2Ba \begin{array}{c} {E.GydF4y2Ba}^{T.GydF4y2Ba} & {E.GydF4y2Ba}^{一种GydF4y2Ba T.GydF4y2Ba} \\ 罪GydF4y2Ba （GydF4y2Ba T.GydF4y2Ba ）GydF4y2Ba & COS.GydF4y2Ba （GydF4y2Ba T.GydF4y2Ba ）GydF4y2Ba \end{array} ）GydF4y2Ba$

Find indefinite integrals of the matrix element-wise.

F=int(M,t)

F=GydF4y2Ba
                      
                        $（GydF4y2Ba \begin{array}{c} {E.GydF4y2Ba}^{T.GydF4y2Ba} & \frac{{E.GydF4y2Ba}^{一种GydF4y2Ba T.GydF4y2Ba}}{一种GydF4y2Ba} \\ -GydF4y2Ba COS.GydF4y2Ba （GydF4y2Ba T.GydF4y2Ba ）GydF4y2Ba & 罪GydF4y2Ba （GydF4y2Ba T.GydF4y2Ba ）GydF4y2Ba \end{array} ）GydF4y2Ba$

Apply IgnoreAnalyticConstraints

Open Live Script

定义符号函数一种nd compute its indefinite integral.

symsF（X）GydF4y2Baf（x）= ACOS（COS（x））;f = int（f，x）GydF4y2Ba

F（X）=GydF4y2Ba
                      
                        $XGydF4y2Ba 一种Cos （GydF4y2Ba COS.GydF4y2Ba （GydF4y2Ba XGydF4y2Ba ）GydF4y2Ba ）GydF4y2Ba -GydF4y2Ba \frac{{XGydF4y2Ba}^{2GydF4y2Ba}}{2GydF4y2Ba 标志GydF4y2Ba （GydF4y2Ba 罪GydF4y2Ba （GydF4y2Ba XGydF4y2Ba ）GydF4y2Ba ）GydF4y2Ba}$

By default,intuses strict mathematical rules. These rules do not letint改写GydF4y2Ba一种Cos(cos(x))如GydF4y2BaXGydF4y2Ba。GydF4y2Ba

如果您想要一个简单的实用解决方案，请设置GydF4y2Ba'Ignoreanalyticonstraints'GydF4y2BaT.oT.rue。GydF4y2Ba

f = int（f，x，GydF4y2Ba'Ignoreanalyticonstraints'GydF4y2Ba那T.rue)

F（X）=GydF4y2Ba
                      
                        $\frac{{XGydF4y2Ba}^{2GydF4y2Ba}}{2GydF4y2Ba}$

Ignore Special Cases

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Define a symbolic expression ${XGydF4y2Ba}^{T.GydF4y2Ba}$ 一种nd compute its indefinite integral with respect to the variable $XGydF4y2Ba$ 。GydF4y2Ba

symsXGydF4y2BaT.GydF4y2BaF=int(x^t,x)

F=GydF4y2Ba
                      
                        ${GydF4y2Ba \begin{array}{cl} \log （GydF4y2Ba XGydF4y2Ba ）GydF4y2Ba & 如果GydF4y2Ba T.GydF4y2Ba =GydF4y2Ba -GydF4y2Ba 1GydF4y2Ba \\ \frac{{XGydF4y2Ba}^{T.GydF4y2Ba +GydF4y2Ba 1GydF4y2Ba}}{T.GydF4y2Ba +GydF4y2Ba 1GydF4y2Ba} & 如果GydF4y2Ba T.GydF4y2Ba \neq -GydF4y2Ba 1GydF4y2Ba \end{array}$

By default,int回报T.he general results for all values of the other symbolic parameterT.GydF4y2Ba。在这个例子中，GydF4y2Baint返回案例的两个积分结果GydF4y2Ba $T.GydF4y2Ba =GydF4y2Ba -GydF4y2Ba 1GydF4y2Ba$ 一种nd $T.GydF4y2Ba \neq -GydF4y2Ba 1GydF4y2Ba$ 。GydF4y2Ba

To ignore special cases of parameter values, set'IgnoreSpecialCase'GydF4y2BaT.oT.rue。W.ith this option,intignores the special case $T.GydF4y2Ba =GydF4y2Ba -GydF4y2Ba 1GydF4y2Ba$ 一种nd returns the solution for $T.GydF4y2Ba \neq -GydF4y2Ba 1GydF4y2Ba$ 。GydF4y2Ba

F=int(x^t,x,'IgnoreSpecialCase'GydF4y2Ba那T.rue)

F=GydF4y2Ba
                      
                        $\frac{{XGydF4y2Ba}^{T.GydF4y2Ba +GydF4y2Ba 1GydF4y2Ba}}{T.GydF4y2Ba +GydF4y2Ba 1GydF4y2Ba}$

找到cauchy主值GydF4y2Ba

Open Live Script

定义符号函数GydF4y2Ba $FGydF4y2Ba （GydF4y2Ba XGydF4y2Ba ）GydF4y2Ba =GydF4y2Ba 1GydF4y2Ba /GydF4y2Ba （GydF4y2Ba XGydF4y2Ba -GydF4y2Ba 1GydF4y2Ba ）GydF4y2Ba$ 有一个杆子GydF4y2Ba $XGydF4y2Ba =GydF4y2Ba 1GydF4y2Ba$ 。GydF4y2Ba

symsXGydF4y2Baf（x）= 1 /（x-1）GydF4y2Ba

F（X）=GydF4y2Ba
                      
                        $\frac{1GydF4y2Ba}{XGydF4y2Ba -GydF4y2Ba 1GydF4y2Ba}$

计算此功能的明确积分GydF4y2Ba $XGydF4y2Ba =GydF4y2Ba 0.GydF4y2Ba$ T.o $XGydF4y2Ba =GydF4y2Ba 2GydF4y2Ba$ 。Since the integration interval includes the pole, the result is not defined.

f = int（f，[0 2]）GydF4y2Ba

F=GydF4y2Ba
                       $南GydF4y2Ba$

但是，积分的Cauchy主值存在。计算积分的Cauchy主值，设置GydF4y2Ba'PrincipalValue'T.oT.rue。GydF4y2Ba

f = int（f，[0 2]，GydF4y2Ba'PrincipalValue'那T.rue)

F=GydF4y2Ba
                       $0.GydF4y2Ba$

Unevaluated Integral and Integration by Parts

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Find the integral of $\int XGydF4y2Ba {E.GydF4y2Ba}^{XGydF4y2Ba} DX.GydF4y2Ba$ 。GydF4y2Ba

Define the integral without evaluating it by setting the'Hold'option toT.rue。GydF4y2Ba

symsXGydF4y2BaG（y)f = int（x * exp（x），GydF4y2Ba'Hold'那T.rue)

F=GydF4y2Ba
                      
                        $\int XGydF4y2Ba {E.GydF4y2Ba}^{XGydF4y2Ba} D.GydF4y2Ba XGydF4y2Ba$

您可以按零部件应用集成GydF4y2BaFGydF4y2BaB.y using theIntegrateByparts.GydF4y2Ba功能。UseE.Xp(x)如T.he differential to be integrated.

G=IntegrateByparts.（F那E.Xp(x))

G=GydF4y2Ba
                      
                        $XGydF4y2Ba {E.GydF4y2Ba}^{XGydF4y2Ba} -GydF4y2Ba \int {E.GydF4y2Ba}^{XGydF4y2Ba} D.GydF4y2Ba XGydF4y2Ba$

评估积分的GydF4y2BaGGydF4y2Ba，使用GydF4y2Ba释放GydF4y2BaFunction to ignore the'Hold'option.

gcalc =释放（g）GydF4y2Ba

GC一种lc =
                       $XGydF4y2Ba {E.GydF4y2Ba}^{XGydF4y2Ba} -GydF4y2Ba {E.GydF4y2Ba}^{XGydF4y2Ba}$

Compare the result to the integration result returned byintwithout setting the'Hold'option.

fcalc = int（x * exp（x））GydF4y2Ba

FC一种lc =
                       ${E.GydF4y2Ba}^{XGydF4y2Ba} (XGydF4y2Ba -GydF4y2Ba 1GydF4y2Ba)$

近似无限度积分GydF4y2Ba

Open Live Script

如果GydF4y2Baint无法计算封闭形式的积分，然后它返回一个未解决的积分。GydF4y2Ba

symsF（X）GydF4y2BaF（X）=罪（罪h(x)); F = int(f,x)

F（X）=GydF4y2Ba
                      
                        $\int 罪GydF4y2Ba （GydF4y2Ba 罪h （GydF4y2Ba XGydF4y2Ba ）GydF4y2Ba ）GydF4y2Ba D.GydF4y2Ba XGydF4y2Ba$

You can approximate the integrand function $FGydF4y2Ba （GydF4y2Ba XGydF4y2Ba ）GydF4y2Ba$ 如polynomials by using the Taylor expansion. ApplyT.一种ylor扩展Integrand函数GydF4y2Ba $FGydF4y2Ba （GydF4y2Ba XGydF4y2Ba ）GydF4y2Ba$ 如polynomials around $XGydF4y2Ba =GydF4y2Ba 0.GydF4y2Ba$ 。计算近似多项式的积分。GydF4y2Ba

ftaylor =泰勒（f，x，GydF4y2Ba'ExpansionPoint'那0.那GydF4y2Ba'Order'那10.）GydF4y2Ba

FTaylor(x) =
                      
                        $\frac{{XGydF4y2Ba}^{9.GydF4y2Ba}}{5670.GydF4y2Ba} -GydF4y2Ba \frac{{XGydF4y2Ba}^{7.GydF4y2Ba}}{9.0.GydF4y2Ba} -GydF4y2Ba \frac{{XGydF4y2Ba}^{5.GydF4y2Ba}}{15.GydF4y2Ba} +GydF4y2Ba XGydF4y2Ba$

F一种pprox = int(fTaylor,x)

F一种pprox(x) =
                      
                        $\frac{{XGydF4y2Ba}^{10.GydF4y2Ba}}{56700GydF4y2Ba} -GydF4y2Ba \frac{{XGydF4y2Ba}^{8.GydF4y2Ba}}{720.GydF4y2Ba} -GydF4y2Ba \frac{{XGydF4y2Ba}^{6.GydF4y2Ba}}{9.0.GydF4y2Ba} +GydF4y2Ba \frac{{XGydF4y2Ba}^{2GydF4y2Ba}}{2GydF4y2Ba}$

输入参数GydF4y2Ba

全部收缩GydF4y2Ba

`E.Xpr`-GydF4y2Ba整合GydF4y2Ba
symbolic expression|GydF4y2Basymbolic function|GydF4y2Ba符号矢量GydF4y2Ba|GydF4y2Basymbolic matrix|GydF4y2Basymbolic number

Integrand，指定为符号表达式，函数，矢量，矩阵或数字。GydF4y2Ba

`var`-GydF4y2Ba集成变量GydF4y2Ba
symbolic variable

集成变量指定为一个象征性的变化一种B.le. If you do not specify this variable,intuses the default variable determined bySymvar（expr，1）GydF4y2Ba。如果GydF4y2BaE.Xpris a constant, then the default variable isXGydF4y2Ba。GydF4y2Ba

`一种GydF4y2Ba`-GydF4y2Ba下限GydF4y2Ba
数GydF4y2Ba|GydF4y2Basymbolic number|GydF4y2Basymbolic variable|GydF4y2Basymbolic expression|GydF4y2Basymbolic function

下限，指定为数字，符号编号，变量，表达式或函数（包括具有Infinities的表达式和函数）。GydF4y2Ba

`B.GydF4y2Ba`-GydF4y2Ba上限GydF4y2Ba
数GydF4y2Ba|GydF4y2Basymbolic number|GydF4y2Basymbolic variable|GydF4y2Basymbolic expression|GydF4y2Basymbolic function

上限那specified as a number, symbolic number, variable, expression, or function (including expressions and functions with infinities).

名称值对参数GydF4y2Ba

指定可选的逗号分离对GydF4y2Ba名称，价值GydF4y2Ba一种rguments.Name是参数名称和GydF4y2BaValueis the corresponding value.Name必须出现在引号内。您可以以任何顺序指定多个名称和值对参数GydF4y2BaName1,Value1,...,NameN,ValueN。GydF4y2Ba

Example:'Ignoreanalyticonstraints'那T.rue指定GydF4y2Baint一种pplies purely algebraic simplifications to the integrand.

`'Ignoreanalyticonstraints'GydF4y2Ba`-GydF4y2BaIndicator for applying purely algebraic simplifications to integrand
`假GydF4y2Ba`（D.E.F一种ult) |`T.rue`

用于将纯粹代数简化应用于整合的指示器，指定为GydF4y2BaT.rueor假GydF4y2Ba。如果T.he value isT.rue，将纯粹的代数简化应用于整合和平。此选项可以为表达式提供更简单的结果，其中Integrator的直接使用返回复杂的结果。在某些情况下，它也可以实现GydF4y2BaintT.o compute integrals that cannot be computed otherwise.

Using this option can lead to results not generally valid. This option applies mathematical identities that are convenient, but the results do not always hold for all values of variables.

`'IgnoreSpecialCase'GydF4y2Ba`-GydF4y2Ba忽略特殊情况的指标GydF4y2Ba
`假GydF4y2Ba`（D.E.F一种ult) |`T.rue`

忽略特殊情况的指标，指定为GydF4y2BaT.rueor假GydF4y2Ba。这忽略了需要一个或多个参数的案例是相对较小的集合的元素，例如固定的有限集或一组整数。GydF4y2Ba

`'PrincipalValue'`-GydF4y2Ba返回主值的指标GydF4y2Ba
`假GydF4y2Ba`（D.E.F一种ult) |`T.rue`

Indicator for returning the principal value, specified asT.rueor假GydF4y2Ba。如果T.he value isT.rue那Compute the Cauchy principal value of the integral. In live script, the Cauchy principal value of unevaluated integral shows as the符号。GydF4y2Ba

`'Hold'`-GydF4y2BaIndicator for unevaluated integration
`假GydF4y2Ba`（D.E.F一种ult) |`T.rue`

Indicator for unevaluated integration, specified asT.rueor假GydF4y2Ba。如果T.he value isT.rue那GydF4y2Baint回报integrals without evaluating them.

Tips

与分化相比，符号集成是一个更复杂的任务。如果GydF4y2BaintC一种nnot compute an integral of an expression, check for these reasons:
- The antiderivative does not exist in a closed form.
- The antiderivative exists, butint找不到。GydF4y2Ba
如果GydF4y2Baint无法计算封闭形式的积分，它返回一个未解决的积分。GydF4y2Ba
Try approximating such integrals by using one of these methods:
- For indefinite integrals, use series expansions. Use this method to approximate an integral around a particular value of the variable.
- For definite integrals, use numeric approximations.
For indefinite integrals,intD.oes not return a constant of integration in the result. The results of integrating mathematically equivalent expressions may be different. For example,Syms X;int（（x + 1）^ 2）GydF4y2Ba回报GydF4y2Ba（X+1）^3/3那whileSyms X;int(x^2+2*x+1)回报GydF4y2Ba（X*(x^2+3*x+3))/3那which differs from the first result by1/3。GydF4y2Ba
For indefinite integrals,intimplicitly assumes that the integration variablevaris real. For definite integrals,int限制集成变量GydF4y2BavarT.o the specified integration interval. If one or both integration bounds一种GydF4y2Ba一种ndB.GydF4y2Ba不是数字，GydF4y2Baint如sumes thata <= bGydF4y2Ba除非您明确指定另有说明。GydF4y2Ba

算法GydF4y2Ba

W.hen you useIgnoreAnalyticConstraints那GydF4y2Baint一种pplies these rules:

日志（GydF4y2Ba一种GydF4y2Ba）+日志（GydF4y2BaB.GydF4y2Ba）=日志（GydF4y2Ba一种GydF4y2Ba·GydF4y2BaB.GydF4y2Ba）GydF4y2BaFor all values of一种GydF4y2Ba一种ndB.GydF4y2Ba。In particular, the following equality is valid for all values of一种GydF4y2Ba那GydF4y2BaB.GydF4y2Ba那一种ndCGydF4y2Ba：GydF4y2Ba
（GydF4y2Ba一种GydF4y2Ba·GydF4y2BaB.GydF4y2Ba）GydF4y2Ba^CGydF4y2Ba=GydF4y2Ba一种GydF4y2Ba^CGydF4y2Ba·GydF4y2BaB.GydF4y2Ba^CGydF4y2Ba。GydF4y2Ba
日志（GydF4y2Ba一种GydF4y2Ba^B.GydF4y2Ba）=GydF4y2BaB.GydF4y2Ba·日志（GydF4y2Ba一种GydF4y2Ba）GydF4y2BaFor all values of一种GydF4y2Ba一种ndB.GydF4y2Ba。In particular, the following equality is valid for all values of一种GydF4y2Ba那GydF4y2BaB.GydF4y2Ba那一种ndCGydF4y2Ba：GydF4y2Ba
（GydF4y2Ba一种GydF4y2Ba^B.GydF4y2Ba）GydF4y2Ba^CGydF4y2Ba=GydF4y2Ba一种GydF4y2Ba^{B.GydF4y2Ba·GydF4y2BaCGydF4y2Ba}。GydF4y2Ba
如果GydF4y2BaFGydF4y2Ba一种ndGGydF4y2Ba一种re standard mathematical functions andFGydF4y2Ba（GydF4y2BaGGydF4y2Ba（GydF4y2BaXGydF4y2Ba））=GydF4y2BaXGydF4y2Ba对于所有小的阳性数字，那么GydF4y2BaFGydF4y2Ba（GydF4y2BaGGydF4y2Ba（GydF4y2BaXGydF4y2Ba））=GydF4y2BaXGydF4y2Bais assumed to be valid for all complex valuesXGydF4y2Ba。In particular:
- 日志（GydF4y2BaE.GydF4y2Ba^XGydF4y2Ba）=GydF4y2BaXGydF4y2Ba
- asin（罪恶（GydF4y2BaXGydF4y2Ba））=GydF4y2BaXGydF4y2Ba那GydF4y2Ba一种Cos(cos(XGydF4y2Ba））=GydF4y2BaXGydF4y2Ba那GydF4y2Baatan（棕褐色（GydF4y2BaXGydF4y2Ba））=GydF4y2BaXGydF4y2Ba
- Asinh（SINH（GydF4y2BaXGydF4y2Ba））=GydF4y2BaXGydF4y2Ba那GydF4y2Ba一种Cosh(cosh(XGydF4y2Ba））=GydF4y2BaXGydF4y2Ba那GydF4y2Ba一种T.一种nh(tanh(XGydF4y2Ba））=GydF4y2BaXGydF4y2Ba
- W.GydF4y2Ba_K.GydF4y2Ba（GydF4y2BaXGydF4y2Ba·GydF4y2BaE.GydF4y2Ba^XGydF4y2Ba）=GydF4y2BaXGydF4y2Ba对于所有分支指数GydF4y2BaK.GydF4y2Baof the LambertW.GydF4y2Ba功能。GydF4y2Ba

也可以看看GydF4y2Ba

话题GydF4y2Ba

Integration

Introduced before R2006a

int

句法GydF4y2Ba

Description

Examples

无限制的单变量表达的积分GydF4y2Ba

多元函数的无限积分GydF4y2Ba

Definite Integrals of Symbolic Expressions

矩阵元素的积分GydF4y2Ba

Apply IgnoreAnalyticConstraints

Ignore Special Cases

找到cauchy主值GydF4y2Ba

Unevaluated Integral and Integration by Parts

近似无限度积分GydF4y2Ba

输入参数GydF4y2Ba

`E.Xpr`-GydF4y2Ba整合GydF4y2Ba
symbolic expression|GydF4y2Basymbolic function|GydF4y2Ba符号矢量GydF4y2Ba|GydF4y2Basymbolic matrix|GydF4y2Basymbolic number

`var`-GydF4y2Ba集成变量GydF4y2Ba
symbolic variable

`一种GydF4y2Ba`-GydF4y2Ba下限GydF4y2Ba
数GydF4y2Ba|GydF4y2Basymbolic number|GydF4y2Basymbolic variable|GydF4y2Basymbolic expression|GydF4y2Basymbolic function

`B.GydF4y2Ba`-GydF4y2Ba上限GydF4y2Ba
数GydF4y2Ba|GydF4y2Basymbolic number|GydF4y2Basymbolic variable|GydF4y2Basymbolic expression|GydF4y2Basymbolic function

名称值对参数GydF4y2Ba

`'Ignoreanalyticonstraints'GydF4y2Ba`-GydF4y2BaIndicator for applying purely algebraic simplifications to integrand
`假GydF4y2Ba`（D.E.F一种ult) |`T.rue`

`'IgnoreSpecialCase'GydF4y2Ba`-GydF4y2Ba忽略特殊情况的指标GydF4y2Ba
`假GydF4y2Ba`（D.E.F一种ult) |`T.rue`

`'PrincipalValue'`-GydF4y2Ba返回主值的指标GydF4y2Ba
`假GydF4y2Ba`（D.E.F一种ult) |`T.rue`

`'Hold'`-GydF4y2BaIndicator for unevaluated integration
`假GydF4y2Ba`（D.E.F一种ult) |`T.rue`

Tips

算法GydF4y2Ba

也可以看看GydF4y2Ba

话题GydF4y2Ba

象征性的Math Toolbox Documentation

金宝app

Mathematical Modeling with Symbolic Math Toolbox

int

句法GydF4y2Ba

Description

Examples

无限制的单变量表达的积分GydF4y2Ba

多元函数的无限积分GydF4y2Ba

Definite Integrals of Symbolic Expressions

矩阵元素的积分GydF4y2Ba

Apply IgnoreAnalyticConstraints

Ignore Special Cases

找到cauchy主值GydF4y2Ba

Unevaluated Integral and Integration by Parts

近似无限度积分GydF4y2Ba

输入参数GydF4y2Ba

E.Xpr-GydF4y2Ba整合GydF4y2Basymbolic expression|GydF4y2Basymbolic function|GydF4y2Ba符号矢量GydF4y2Ba|GydF4y2Basymbolic matrix|GydF4y2Basymbolic number

var-GydF4y2Ba集成变量GydF4y2Basymbolic variable

一种GydF4y2Ba-GydF4y2Ba下限GydF4y2Ba数GydF4y2Ba|GydF4y2Basymbolic number|GydF4y2Basymbolic variable|GydF4y2Basymbolic expression|GydF4y2Basymbolic function

B.GydF4y2Ba-GydF4y2Ba上限GydF4y2Ba数GydF4y2Ba|GydF4y2Basymbolic number|GydF4y2Basymbolic variable|GydF4y2Basymbolic expression|GydF4y2Basymbolic function

名称值对参数GydF4y2Ba

'Ignoreanalyticonstraints'GydF4y2Ba-GydF4y2BaIndicator for applying purely algebraic simplifications to integrand假GydF4y2Ba（D.E.F一种ult) |T.rue

'IgnoreSpecialCase'GydF4y2Ba-GydF4y2Ba忽略特殊情况的指标GydF4y2Ba假GydF4y2Ba（D.E.F一种ult) |T.rue

'PrincipalValue'-GydF4y2Ba返回主值的指标GydF4y2Ba假GydF4y2Ba（D.E.F一种ult) |T.rue

'Hold'-GydF4y2BaIndicator for unevaluated integration假GydF4y2Ba（D.E.F一种ult) |T.rue

Tips

算法GydF4y2Ba

也可以看看GydF4y2Ba

话题GydF4y2Ba

象征性的Math Toolbox Documentation

金宝app

Mathematical Modeling with Symbolic Math Toolbox

`E.Xpr`-GydF4y2Ba整合GydF4y2Ba
symbolic expression|GydF4y2Basymbolic function|GydF4y2Ba符号矢量GydF4y2Ba|GydF4y2Basymbolic matrix|GydF4y2Basymbolic number

`var`-GydF4y2Ba集成变量GydF4y2Ba
symbolic variable

`一种GydF4y2Ba`-GydF4y2Ba下限GydF4y2Ba
数GydF4y2Ba|GydF4y2Basymbolic number|GydF4y2Basymbolic variable|GydF4y2Basymbolic expression|GydF4y2Basymbolic function

`B.GydF4y2Ba`-GydF4y2Ba上限GydF4y2Ba
数GydF4y2Ba|GydF4y2Basymbolic number|GydF4y2Basymbolic variable|GydF4y2Basymbolic expression|GydF4y2Basymbolic function

`'Ignoreanalyticonstraints'GydF4y2Ba`-GydF4y2BaIndicator for applying purely algebraic simplifications to integrand
`假GydF4y2Ba`（D.E.F一种ult) |`T.rue`

`'IgnoreSpecialCase'GydF4y2Ba`-GydF4y2Ba忽略特殊情况的指标GydF4y2Ba
`假GydF4y2Ba`（D.E.F一种ult) |`T.rue`

`'PrincipalValue'`-GydF4y2Ba返回主值的指标GydF4y2Ba
`假GydF4y2Ba`（D.E.F一种ult) |`T.rue`

`'Hold'`-GydF4y2BaIndicator for unevaluated integration
`假GydF4y2Ba`（D.E.F一种ult) |`T.rue`