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

Factor out common term

- 3

= \int - 3 (tan^{2} (θ) + 1) d θ

Take the constant out:

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

= - 3 \cdot \int tan^{2} (θ) + 1 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