What is the integral of sec(x)tan(x)sqrt(1+sec(x)) ?

The integral of sec(x)tan(x)sqrt(1+sec(x)) is 2/3 (1+sec(x))^{3/2}+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)sqrt(1+sec(x))

\int sec (x) tan (x) 1 + sec (x) d x

\frac{2}{3} (1 + sec (x))^{\frac{3}{2}} + C

Solution steps

\int sec (x) tan (x) 1 + sec (x) d x

Apply u-substitution

= \int u d u

Apply the Power Rule

= \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 1 + sec (x)

= \frac{2}{3} (1 + sec (x))^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (1 + sec (x))^{\frac{3}{2}} + C

What is the integral of sec(x)tan(x)sqrt(1+sec(x)) ?
The integral of sec(x)tan(x)sqrt(1+sec(x)) is 2/3 (1+sec(x))^{3/2}+C