What is the integral of t^4cos(t^5) ?

The integral of t^4cos(t^5) is 1/5 sin(t^5)+C

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integral of t^4cos(t^5)

\int t^{4} cos (t^{5}) d t

\frac{1}{5} sin (t^{5}) + C

Solution steps

\int t^{4} cos (t^{5}) d t

Apply u-substitution

: \int \frac{cos ( u )}{5} d u

= \int \frac{cos ( u )}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= \frac{1}{5} sin (u)

Substitute back

u = t^{5}

= \frac{1}{5} sin (t^{5})

Add a constant to the solution

= \frac{1}{5} sin (t^{5}) + C

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What is the integral of t^4cos(t^5) ?
The integral of t^4cos(t^5) is 1/5 sin(t^5)+C