How do you find the integral of $sin^2 (5x)$ ?

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Answer 1 · 2017-10-03T20:41:50

$int (sin5x)^2*dx$

= $int 1/2*(1-cos10x)*dx$

= $1/2$ $int dx$ - $1/2$ $int cos10x*dx$

= $x/2-1/20*sin10x+C$

1) I used $(sinax)^2=1/2*(1-cos2ax)$ identity.

2) I used distribution rule of integral.

3) I found solution of it.

How do you find the integral of sin^2 (5x)sin^2 (5x)?