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

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

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integral of (1+tan^2(a))

\int (1 + tan^{2} (a)) d a

tan (a) + C

Solution steps

\int 1 + tan^{2} (a) d a

Rewrite using trig identities

= \int sec^{2} (a) d a

Use the common integral:

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

= tan (a)

Add a constant to the solution

= tan (a) + C

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