release

Evaluate integrals

Description

example

release(expr) evaluates the integrals in the expression expr. The release function ignores the 'Hold' option in the int function when the integrals are defined.

Examples

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Define a symbolic call to an integral cos(x)dx without evaluating it. Set the 'Hold' option to true when defining the integral using the int function.

syms x
F = int(cos(x),'Hold',true)
F = 

cos(x)dx

Use release to evaluate the integral by ignoring the 'Hold' option.

G = release(F)
G = sin(x)

Find the integral of xexdx.

Define the integral without evaluating it by setting the 'Hold' option to true.

syms x g(y)
F = int(x*exp(x),'Hold',true)
F = 

xexdx

You can apply integration by parts to F by using the integrateByParts function. Use exp(x) as the differential to be integrated.

G = integrateByParts(F,exp(x))
G = 

xex-exdx

To evaluate the integral in G, use the release function to ignore the 'Hold' option.

Gcalc = release(G)
Gcalc = xex-ex

Compare the result to the integration result returned by int without setting the 'Hold' option.

Fcalc = int(x*exp(x))
Fcalc = exx-1

Find the integral of cos(log(x))dx using integration by substitution.

Define the integral without evaluating it by setting the 'Hold' option to true.

syms x t
F = int(cos(log(x)),'Hold',true)
F = 

cos(log(x))dx

Substitute the expression log(x) with t.

G = changeIntegrationVariable(F,log(x),t) 
G = 

etcos(t)dt

To evaluate the integral in G, use the release function to ignore the 'Hold' option.

H = release(G)
H = 

etcos(t)+sin(t)2

Restore log(x) in place of t.

H = simplify(subs(H,t,log(x)))
H = 

2xsin(π4+log(x))2

Compare the result to the integration result returned by int without setting the 'Hold' option to true.

Fcalc = int(cos(log(x)))
Fcalc = 

2xsin(π4+log(x))2

Input Arguments

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Expression containing integrals, specified as a symbolic expression, function, vector, or matrix.

Introduced in R2019b