What is the integral of (3sin(x))^2 ?

The integral of (3sin(x))^2 is 9xsin^2(x)-9(-1/2 xcos(2x)+1/4 sin(2x))+C

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integral of (3sin(x))^2

\int (3 sin (x))^{2} d x

9 x sin^{2} (x) - 9 (- \frac{1}{2} x cos (2 x) + \frac{1}{4} sin (2 x)) + C

Solution steps

\int (3 sin (x))^{2} d x

Apply Integration By Parts

: 9 x sin^{2} (x) - \int 9 x sin (2 x) d x

= 9 x sin^{2} (x) - \int 9 x sin (2 x) d x

\int 9 x sin (2 x) d x = 9 (- \frac{1}{2} x cos (2 x) + \frac{1}{4} sin (2 x))

= 9 x sin^{2} (x) - 9 (- \frac{1}{2} x cos (2 x) + \frac{1}{4} sin (2 x))

Add a constant to the solution

= 9 x sin^{2} (x) - 9 (- \frac{1}{2} x cos (2 x) + \frac{1}{4} sin (2 x)) + C

\int \frac{1}{3 x - 2} d x

\frac{d}{d x} (12 cos (3 x))

\frac{d y}{d x}, 4 x^{2} + 6 y^{2} = 24 x

\int (x - 3)^{6} d x

\frac{d}{d x} ((a - b x)^{2})

What is the integral of (3sin(x))^2 ?
The integral of (3sin(x))^2 is 9xsin^2(x)-9(-1/2 xcos(2x)+1/4 sin(2x))+C