Question

Evaluate the indefinite integral. (Use C for the constant of integration.) sin(10x) 1 cos2(10x) dx

Answer 1

The result of the integral is
`-\frac{\cos^3{10x}}{30} + C`

Explanation:

We are given the following integral:

`\int sin((10x))\cos^(2){(10x)} dx`

I am going to solve by substitution, using
`u = cos(10x)`, so
`du = -10sin(10x)dx, dx = -(du)/(10sin(10x))`. So, we have

`-(1)/(10) \int u^2 du`

Which has the following result:

`-(u^3)/(30) + C`

Going back to x, the result of the integral is

`-\frac{\cos^3{10x}}{30} + C`