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

The integral of (2cos(x)+sec^2(x)) is 2sin(x)+tan(x)+C

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

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

2 sin (x) + tan (x) + C

Solution steps

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

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

\int sec^{2} (x) d x = tan (x)

= 2 sin (x) + tan (x)

Add a constant to the solution

= 2 sin (x) + tan (x) + C

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