What is the integral of tan^{1/2}(x)sec^2(x) ?

The integral of tan^{1/2}(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 tan^{1/2}(x)sec^2(x)

\int tan^{\frac{1}{2}} (x) 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 x^{2} e^{\frac{x ^{3}}{2}} d x

\int - \frac{a}{x ^{2}} d x

\int 2 x cos (3 x + 1) d x

\int 9 cos (x) - 4 sin (x) d x

\int (9 x^{2} - 9 x + 2) d x

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