What is the integral of x^{35}sin(x^{36}) ?

The integral of x^{35}sin(x^{36}) is -1/36 cos(x^{36})+C

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integral of x^{35}sin(x^{36})

\int x^{35} sin (x^{36}) d x

- \frac{1}{36} cos (x^{36}) + C

Solution steps

\int x^{35} sin (x^{36}) d x

Apply u-substitution

: \int \frac{sin ( u )}{36} d u

= \int \frac{sin ( u )}{36} d u

Take the constant out:

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

= \frac{1}{36} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{36} (- cos (u))

Substitute back

u = x^{36}

= \frac{1}{36} (- cos (x^{36}))

Simplify

= - \frac{1}{36} cos (x^{36})

Add a constant to the solution

= - \frac{1}{36} cos (x^{36}) + C

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What is the integral of x^{35}sin(x^{36}) ?
The integral of x^{35}sin(x^{36}) is -1/36 cos(x^{36})+C