What is the integral of (1+tan^2(θ)) ?

The integral of (1+tan^2(θ)) is tan(θ)+C

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integral of (1+tan^2(θ))

\int (1 + tan^{2} (θ)) d θ

tan (θ) + C

Solution steps

\int 1 + tan^{2} (θ) d θ

Rewrite using trig identities

= \int sec^{2} (θ) d θ

Use the common integral:

\int sec^{2} (θ) d θ = tan (θ)

= tan (θ)

Add a constant to the solution

= tan (θ) + C

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