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# release

Evaluate integrals

## Syntax

``release(expr)``

## 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 $\int \mathrm{cos}\left(\mathit{x}\right)\text{\hspace{0.17em}}\mathit{dx}$ 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 =  $\int \mathrm{cos}\left(x\right)\mathrm{d}x$```

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

`G = release(F)`
`G = $\mathrm{sin}\left(x\right)$`

Find the integral of $\int \mathit{x}\text{\hspace{0.17em}}{\mathit{e}}^{\mathit{x}}\text{\hspace{0.17em}}\mathit{dx}$.

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 =  $\int x {\mathrm{e}}^{x}\mathrm{d}x$```

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 =  $x {\mathrm{e}}^{x}-\int {\mathrm{e}}^{x}\mathrm{d}x$```

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

`Gcalc = release(G)`
`Gcalc = $x {\mathrm{e}}^{x}-{\mathrm{e}}^{x}$`

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

`Fcalc = int(x*exp(x))`
`Fcalc = ${\mathrm{e}}^{x} \left(x-1\right)$`

Find the integral of $\int \mathrm{cos}\left(\mathrm{log}\left(\mathit{x}\right)\right)\mathit{dx}$ 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 =  $\int \mathrm{cos}\left(\mathrm{log}\left(x\right)\right)\mathrm{d}x$```

Substitute the expression `log(x)` with `t`.

`G = changeIntegrationVariable(F,log(x),t) `
```G =  $\int {\mathrm{e}}^{t} \mathrm{cos}\left(t\right)\mathrm{d}t$```

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

`H = release(G)`
```H =  $\frac{{\mathrm{e}}^{t} \left(\mathrm{cos}\left(t\right)+\mathrm{sin}\left(t\right)\right)}{2}$```

Restore `log(x)` in place of `t`.

`H = simplify(subs(H,t,log(x)))`
```H =  $\frac{\sqrt{2} x \mathrm{sin}\left(\frac{\pi }{4}+\mathrm{log}\left(x\right)\right)}{2}$```

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

`Fcalc = int(cos(log(x)))`
```Fcalc =  $\frac{\sqrt{2} x \mathrm{sin}\left(\frac{\pi }{4}+\mathrm{log}\left(x\right)\right)}{2}$```

## Input Arguments

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

## See Also

Introduced in R2019b

## Support

#### Mathematical Modeling with Symbolic Math Toolbox

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