What is the integral of (2sin(x))^2 ?

The integral of (2sin(x))^2 is 4xsin^2(x)+2xcos(2x)-sin(2x)+C

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integral of (2sin(x))^2

\int (2 sin (x))^{2} d x

4 x sin^{2} (x) + 2 x cos (2 x) - sin (2 x) + C

Solution steps

\int (2 sin (x))^{2} d x

Apply Integration By Parts

: 4 x sin^{2} (x) - \int 4 x sin (2 x) d x

= 4 x sin^{2} (x) - \int 4 x sin (2 x) d x

\int 4 x sin (2 x) d x = - 2 x cos (2 x) + sin (2 x)

= 4 x sin^{2} (x) - (- 2 x cos (2 x) + sin (2 x))

Simplify

= 4 x sin^{2} (x) + 2 x cos (2 x) - sin (2 x)

Add a constant to the solution

= 4 x sin^{2} (x) + 2 x cos (2 x) - sin (2 x) + C

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What is the integral of (2sin(x))^2 ?
The integral of (2sin(x))^2 is 4xsin^2(x)+2xcos(2x)-sin(2x)+C