What is the integral of 4/5 sec(x)tan(x) ?

The integral of 4/5 sec(x)tan(x) is 4/5 sec(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 4/5 sec(x)tan(x)

\int \frac{4}{5} sec (x) tan (x) d x

\frac{4}{5} sec (x) + C

Solution steps

\int \frac{4}{5} sec (x) tan (x) d x

Take the constant out:

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

= \frac{4}{5} \cdot \int sec (x) tan (x) d x

Apply u-substitution

= \frac{4}{5} \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= \frac{4}{5} \cdot 1 \cdot u

Substitute back

u = sec (x)

= \frac{4}{5} \cdot 1 \cdot sec (x)

Simplify

= \frac{4}{5} sec (x)

Add a constant to the solution

= \frac{4}{5} sec (x) + C

What is the integral of 4/5 sec(x)tan(x) ?
The integral of 4/5 sec(x)tan(x) is 4/5 sec(x)+C