What is the integral of x^7cos(x^8) ?

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

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integral of x^7cos(x^8)

\int x^{7} cos (x^{8}) d x

\frac{1}{8} sin (x^{8}) + C

Solution steps

\int x^{7} cos (x^{8}) d x

Apply u-substitution

= \int \frac{cos ( u )}{8} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{8} sin (u)

Substitute back

u = x^{8}

= \frac{1}{8} sin (x^{8})

Add a constant to the solution

= \frac{1}{8} sin (x^{8}) + C

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