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

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

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

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

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

Solution steps

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

\int 2 x cos (x) d x = 2 (x sin (x) + cos (x))

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

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

Add a constant to the solution

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

\int_{0}^{2} \frac{2}{16 - x ^{2}} d x

\int cot^{3} (4 x) d x

f (x) = \frac{4 x}{x + 2}, at x = 6

\frac{d}{d x} (3 x + 8)

\int cos^{2} (x t a) n^{3} x d x

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