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

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

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integral of t^5cos(t^6)

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

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

Solution steps

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

Apply u-substitution

: \int \frac{cos ( u )}{6} d u

= \int \frac{cos ( u )}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{6} sin (u)

Substitute back

u = t^{6}

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

Add a constant to the solution

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

\int arcsin (\frac{x}{3}) d x

\int \frac{- 3 x - 1}{x ^{2} + 1} d x

\int 2 e^{\frac{x}{y}} d x

\int \frac{49 - x ^{2}}{4 x ^{2}} d x

\int (\frac{2 x}{3})^{2} d x

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