Answer:
The result of the integral is [tex]-\frac{\cos^3{10x}}{30} + C[/tex]
Step-by-step explanation:
We are given the following integral:
[tex]\int \sin{(10x)}\cos^{2}{(10x)} dx[/tex]
I am going to solve by substitution, using [tex]u = \cos{10x}[/tex], so [tex]du = -10\sin{10x}dx, dx = -\frac{du}{10\sin{10x}}[/tex]. So, we have
[tex]-\frac{1}{10} \int u^2 du[/tex]
Which has the following result:
[tex]-\frac{u^3}{30} + C[/tex]
Going back to x, the result of the integral is
[tex]-\frac{\cos^3{10x}}{30} + C[/tex]
