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

The integral of (rivative of cos(x))^2 is x derivative of cos(x)^2+1/2 xcos(2x)-1/4 sin(2x)+C

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Simplify

\frac{d}{d x} (cos (x))^{2} x - (- \frac{1}{2} x cos (2 x) + \frac{1}{4} sin (2 x)) : x \frac{d}{d x} (cos (x))^{2} + \frac{1}{2} x cos (2 x) - \frac{1}{4} sin (2 x)

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

Add a constant to the solution

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

- (x) + 4

9 m^{3} - 27 m - 6 m + 1

(x^{2} y^{5}) 3

(5.5 x^{4}) + 2298

2 a x - a y + 2 b x - b y

What is the integral of (rivative of cos(x))^2 ?
The integral of (rivative of cos(x))^2 is x derivative of cos(x)^2+1/2 xcos(2x)-1/4 sin(2x)+C