What is the integral of x^{37}sin(x^{38}) ?

The integral of x^{37}sin(x^{38}) is -1/38 cos(x^{38})+C

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integral of x^{37}sin(x^{38})

\int x^{37} sin (x^{38}) d x

- \frac{1}{38} cos (x^{38}) + C

Solution steps

\int x^{37} sin (x^{38}) d x

Apply u-substitution

: \int \frac{sin ( u )}{38} d u

= \int \frac{sin ( u )}{38} d u

Take the constant out:

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

= \frac{1}{38} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{38} (- cos (u))

Substitute back

u = x^{38}

= \frac{1}{38} (- cos (x^{38}))

Simplify

= - \frac{1}{38} cos (x^{38})

Add a constant to the solution

= - \frac{1}{38} cos (x^{38}) + C

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What is the integral of x^{37}sin(x^{38}) ?
The integral of x^{37}sin(x^{38}) is -1/38 cos(x^{38})+C