What is the integral of sqrt(tan(x))*sec^2(x) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sqrt(tan(x))*sec^2(x)

\int tan (x) \cdot sec^{2} (x) d x

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

Solution steps

\int tan (x) sec^{2} (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 = tan (x)

= \frac{2}{3} tan^{\frac{3}{2}} (x)

Add a constant to the solution

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

\int 0.5 e^{- 0.7 x} d x

\int \frac{1}{( 4 x ^{2} + 9 )} d x

\int sin (x) - sin^{2} (x) d x

\int 8 x^{2} + x d x

\int \frac{x + 1}{x ^{2} + x} d x

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