What is the integral of (4+tan^2(θ)) ?

The integral of (4+tan^2(θ)) is 3θ+tan(θ)+C

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integral of (4+tan^2(θ))

\int (4 + tan^{2} (θ)) d θ

3 θ + tan (θ) + C

Solution steps

\int 4 + tan^{2} (θ) 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 4 d θ + \int tan^{2} (θ) d θ

\int 4 d θ = 4 θ

\int tan^{2} (θ) d θ = - θ + tan (θ)

= 4 θ - θ + tan (θ)

Simplify

= 3 θ + tan (θ)

Add a constant to the solution

= 3 θ + tan (θ) + C

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What is the integral of (4+tan^2(θ)) ?
The integral of (4+tan^2(θ)) is 3θ+tan(θ)+C