What is the integral of sec^2(θ)+6 ?

The integral of sec^2(θ)+6 is tan(θ)+6θ+C

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integral of sec^2(θ)+6

\int sec^{2} (θ) + 6 d θ

tan (θ) + 6 θ + C

Solution steps

\int sec^{2} (θ) + 6 d θ

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sec^{2} (θ) d θ + \int 6 d θ

\int sec^{2} (θ) d θ = tan (θ)

\int 6 d θ = 6 θ

= tan (θ) + 6 θ

Add a constant to the solution

= tan (θ) + 6 θ + C