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

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

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integral of cosh(x^2)x

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

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

Solution steps

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

Apply u-substitution

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

= \int \frac{cosh ( 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 cosh (u) d u

Use the common integral:

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

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

Substitute back

u = x^{2}

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

Add a constant to the solution

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

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