Question

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

Answer 1

Answer:

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

Step-by-step 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 $du = -10\sin{10x}dx, dx = -\frac{du}{10\sin{10x}}$. So, we have

$-\frac{1}{10} \int u^2 du$

Which has the following result:

$-\frac{u^3}{30} + C$

Going back to x, the result of the integral is

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