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

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

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integral of xcosh(x^2)

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

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

Solution steps

\int x cosh (x^{2}) 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

\frac{d}{d x} (\frac{x}{2 - x})

\frac{d}{d x} ((x^{2} + 2)^{2} (x^{2} + 2 x + 1)^{3})

2 (12) (5) + 2 (5) \frac{d y}{d t} = 0

\int 11 cot^{4} (x) d x

\int x^{2} cos^{3} (x^{3}) sin^{2} (x^{3}) d x

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