What is the integral of xsinh(x^2) ?

The integral of xsinh(x^2) is 1/2 cosh(x^2)+C

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integral of xsinh(x^2)

\int x sinh (x^{2}) d x

\frac{1}{2} cosh (x^{2}) + C

Solution steps

\int x sinh (x^{2}) d x

Apply u-substitution

: \int \frac{sinh ( u )}{2} d u

= \int \frac{sinh ( u )}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int sinh (u) d u

Use the common integral:

\int sinh (u) d u = cosh (u)

= \frac{1}{2} cosh (u)

Substitute back

u = x^{2}

= \frac{1}{2} cosh (x^{2})

Add a constant to the solution

= \frac{1}{2} cosh (x^{2}) + C

\int 2 + x - x^{2} d x

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\int ln (x + 1) d x

\int \frac{2 ln ∣ x ∣}{x} d x

\int - 2 x^{3} e^{x^{4}} d x

What is the integral of xsinh(x^2) ?
The integral of xsinh(x^2) is 1/2 cosh(x^2)+C