What is the integral of 18θsec^2(θ) ?

The integral of 18θsec^2(θ) is 18(θtan(θ)+ln|cos(θ)|)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 18θsec^2(θ)

\int 18 θ sec^{2} (θ) d θ

18 (θ tan (θ) + ln ∣ cos (θ) ∣) + C

Solution steps

\int 18 θ sec^{2} (θ) d θ

Take the constant out:

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

= 18 \cdot \int θ sec^{2} (θ) d θ

Apply Integration By Parts

= 18 (θ tan (θ) - \int tan (θ) d θ)

\int tan (θ) d θ = - ln ∣ cos (θ) ∣

= 18 (θ tan (θ) - (- ln ∣ cos (θ) ∣))

Simplify

= 18 (θ tan (θ) + ln ∣ cos (θ) ∣)

Add a constant to the solution

= 18 (θ tan (θ) + ln ∣ cos (θ) ∣) + C

What is the integral of 18θsec^2(θ) ?
The integral of 18θsec^2(θ) is 18(θtan(θ)+ln|cos(θ)|)+C