What is the integral of sec(x)tan(x)sqrt(3+sec(x)) ?

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

\int sec (x) tan (x) 3 + sec (x) d x

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

Solution steps

\int sec (x) tan (x) 3 + sec (x) d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

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

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

Substitute back

u = 3 + sec (x)

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

Add a constant to the solution

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

\int x (x^{2} + 3 x - 8) d x

\int \frac{1}{x ^{8} + x} d x

\int (\frac{2}{1 - x ^{2}}) d x

\int \frac{20 ( 1 - x ^{2} )}{x ^{2} + 1} d x

\int (e^{s i n (x)}) d x

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