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

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

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integral of (3+3tan^2(θ))

\int (3 + 3 tan^{2} (θ)) d θ

3 tan (θ) + C

Solution steps

\int 3 + 3 tan^{2} (θ) d θ

3 + 3 tan^{2} (θ) = 3 (1 + tan^{2} (θ))

= \int 3 (1 + tan^{2} (θ)) d θ

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int 1 + tan^{2} (θ) d θ

Rewrite using trig identities

= 3 \cdot \int sec^{2} (θ) d θ

Use the common integral:

\int sec^{2} (θ) d θ = tan (θ)

= 3 tan (θ)

Add a constant to the solution

= 3 tan (θ) + C

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