What is the integral of 4tan^2(θ) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 4tan^2(θ)

\int 4 tan^{2} (θ) d θ

4 (- θ + tan (θ)) + C

Solution steps

\int 4 tan^{2} (θ) d θ

Take the constant out:

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

= 4 \cdot \int tan^{2} (θ) d θ

Rewrite using trig identities

= 4 \cdot \int - 1 + sec^{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

= 4 (- \int 1 d θ + \int sec^{2} (θ) d θ)

\int 1 d θ = θ

\int sec^{2} (θ) d θ = tan (θ)

= 4 (- θ + tan (θ))

Add a constant to the solution

= 4 (- θ + tan (θ)) + C