What is the integral of t^5cos(2t^6) ?

The integral of t^5cos(2t^6) is 1/12 sin(2t^6)+C

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integral of t^5cos(2t^6)

\int t^{5} cos (2 t^{6}) d t

\frac{1}{12} sin (2 t^{6}) + C

Solution steps

\int t^{5} cos (2 t^{6}) d t

Apply u-substitution

: \int \frac{cos ( u )}{12} d u

= \int \frac{cos ( u )}{12} d u

Take the constant out:

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

= \frac{1}{12} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{12} sin (u)

Substitute back

u = 2 t^{6}

= \frac{1}{12} sin (2 t^{6})

Add a constant to the solution

= \frac{1}{12} sin (2 t^{6}) + C

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What is the integral of t^5cos(2t^6) ?
The integral of t^5cos(2t^6) is 1/12 sin(2t^6)+C