What is the integral of tsinh(t^2) ?

The integral of tsinh(t^2) is 1/2 cosh(t^2)+C

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integral of tsinh(t^2)

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

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

Solution steps

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

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 = t^{2}

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

Add a constant to the solution

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

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