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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\int_{2}^{4} 2 π x (- \frac{3}{2} x + 6) d x

\int \frac{x}{2} e^{- \frac{x}{2}} d x

(1 + x^{2}) \cdot \frac{d y}{d x} - \frac{4 x ^{3} y}{1 - x ^{2}} = 1

\int_{0}^{1} \frac{15 5 x + 4}{2} d x

\frac{d y}{d x} - 7 y = e^{x}

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