What is the integral of x^5cos(1-x^6) ?

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

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integral of x^5cos(1-x^6)

\int x^{5} cos (1 - x^{6}) d x

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

Solution steps

\int x^{5} cos (1 - x^{6}) d x

Apply u-substitution

= \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 = 1 - x^{6}

= - \frac{1}{6} sin (1 - x^{6})

Add a constant to the solution

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

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