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

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

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integral of 2+sec^2(x)

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

2 x + tan (x) + C

Solution steps

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

\int 2 d x = 2 x

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

= 2 x + tan (x)

Add a constant to the solution

= 2 x + tan (x) + C