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

The integral of 2tcosh(t^2) is sinh(t^2)+C

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integral of 2tcosh(t^2)

integral

2 t cosh (t^{2})

sinh (t^{2}) + C

Solution steps

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

Take the constant out:

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

= 2 \cdot \int t cosh (t^{2}) d t

Apply u-substitution

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

= 2 \cdot \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

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

Use the common integral:

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

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

Substitute back

u = t^{2}

= 2 \cdot \frac{1}{2} sinh (t^{2})

Simplify

2 \cdot \frac{1}{2} sinh (t^{2}) : sinh (t^{2})

= sinh (t^{2})

Add a constant to the solution

= sinh (t^{2}) + C

\frac{- ( x ^{2} + x )}{2 x + 1}

\frac{( 1 - x ^{8} )}{( 1 - x )}

f (8 - 2 x)

\frac{1}{1 + e ^{x}}

\frac{e ^{x}}{( e ^{x} + 2 )}

What is the integral of 2tcosh(t^2) ?
The integral of 2tcosh(t^2) is sinh(t^2)+C