What is the integral of sec(aθ)tan(aθ) ?

The integral of sec(aθ)tan(aθ) is 1/a sec(aθ)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of sec(aθ)tan(aθ)

\int sec (a θ) tan (a θ) d θ

\frac{1}{a} sec (a θ) + C

Solution steps

\int sec (a θ) tan (a θ) d θ

Apply u-substitution

= \int \frac{sec ( u ) tan ( u )}{a} d u

Take the constant out:

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

= \frac{1}{a} \cdot \int sec (u) tan (u) d u

Apply u-substitution

= \frac{1}{a} \cdot \int 1 d v

Integral of a constant:

\int a d x = a x

= \frac{1}{a} \cdot 1 \cdot v

Substitute back

= \frac{1}{a} \cdot 1 \cdot sec (a θ)

Simplify

= \frac{1}{a} sec (a θ)

Add a constant to the solution

= \frac{1}{a} sec (a θ) + C

What is the integral of sec(aθ)tan(aθ) ?
The integral of sec(aθ)tan(aθ) is 1/a sec(aθ)+C