What is the integral of (sec(x)tan(x))/(sec(x)) ?

The integral of (sec(x)tan(x))/(sec(x)) is ln|sec(x)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (sec(x)tan(x))/(sec(x))

\int \frac{sec ( x ) tan ( x )}{sec ( x )} d x

ln ∣ sec (x) ∣ + C

Solution steps

\int \frac{sec ( x ) tan ( x )}{sec ( x )} d x

Apply u-substitution

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = sec (x)

= ln ∣ sec (x) ∣

Add a constant to the solution

= ln ∣ sec (x) ∣ + C

What is the integral of (sec(x)tan(x))/(sec(x)) ?
The integral of (sec(x)tan(x))/(sec(x)) is ln|sec(x)|+C