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

The integral of (3-2sin(x))^2 is 11x+12cos(x)-sin(2x)+C

integral of (3-2sin(x))^2

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

11 x + 12 cos (x) - sin (2 x) + C

Solution steps

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

Expand

(3 - 2 sin (x))^{2} : 9 - 12 sin (x) + 4 sin^{2} (x)

= \int 9 - 12 sin (x) + 4 sin^{2} (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 9 d x - \int 12 sin (x) d x + \int 4 sin^{2} (x) d x

\int 9 d x = 9 x

\int 12 sin (x) d x = - 12 cos (x)

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

= 9 x - (- 12 cos (x)) + 2 x - sin (2 x)

Simplify

= 11 x + 12 cos (x) - sin (2 x)

Add a constant to the solution

= 11 x + 12 cos (x) - sin (2 x) + C

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What is the integral of (3-2sin(x))^2 ?
The integral of (3-2sin(x))^2 is 11x+12cos(x)-sin(2x)+C