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

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

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integral of cos^2(x)+sin(x)cos(x)

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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