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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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