What is the integral of x^6sin(x^7+8) ?

The integral of x^6sin(x^7+8) is -1/7 cos(x^7+8)+C

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integral of x^6sin(x^7+8)

\int x^{6} sin (x^{7} + 8) d x

- \frac{1}{7} cos (x^{7} + 8) + C

Solution steps

\int x^{6} sin (x^{7} + 8) d x

Apply u-substitution

: \int \frac{sin ( u )}{7} d u

= \int \frac{sin ( u )}{7} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{7} (- cos (u))

Substitute back

u = x^{7} + 8

= \frac{1}{7} (- cos (x^{7} + 8))

Simplify

= - \frac{1}{7} cos (x^{7} + 8)

Add a constant to the solution

= - \frac{1}{7} cos (x^{7} + 8) + C

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What is the integral of x^6sin(x^7+8) ?
The integral of x^6sin(x^7+8) is -1/7 cos(x^7+8)+C