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

The integral of sin(x)-sin^2(x) is -cos(x)-1/2 (x-1/2 sin(2x))+C

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

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

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

Solution steps

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

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

\int sin^{2} (x) d x = \frac{1}{2} (x - \frac{1}{2} sin (2 x))

= - cos (x) - \frac{1}{2} (x - \frac{1}{2} sin (2 x))

Add a constant to the solution

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

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What is the integral of sin(x)-sin^2(x) ?
The integral of sin(x)-sin^2(x) is -cos(x)-1/2 (x-1/2 sin(2x))+C