What is the integral of (sec(x)tan(x))/(sec(x)-5) ?

The integral of (sec(x)tan(x))/(sec(x)-5) is ln|sec(x)-5|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sec(x)tan(x))/(sec(x)-5)

\int \frac{sec ( x ) tan ( x )}{sec ( x ) - 5} d x

ln ∣ sec (x) - 5 ∣ + C

Solution steps

\int \frac{sec ( x ) tan ( x )}{sec ( x ) - 5} d x

Apply u-substitution

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

= \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) - 5

= ln ∣ sec (x) - 5 ∣

Add a constant to the solution

= ln ∣ sec (x) - 5 ∣ + C

\frac{d}{d y} (\frac{x}{y})

x^{2} - 7 x - 24, - x^{2} + 3 x + 4

\frac{\partial}{\partial y} (x - y)

3 ln (5 x)

What is the integral of (sec(x)tan(x))/(sec(x)-5) ?
The integral of (sec(x)tan(x))/(sec(x)-5) is ln|sec(x)-5|+C