What is the integral of (sin(x))^{1/3}cos(x) ?

The integral of (sin(x))^{1/3}cos(x) is 3/4 sin^{4/3}(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (sin(x))^{1/3}cos(x)

\int (sin (x))^{\frac{1}{3}} cos (x) d x

\frac{3}{4} sin^{\frac{4}{3}} (x) + C

Solution steps

\int (sin (x))^{\frac{1}{3}} cos (x) d x

Apply u-substitution

= \int u^{\frac{1}{3}} d u

Apply the Power Rule

= \frac{3}{4} u^{\frac{4}{3}}

Substitute back

u = sin (x)

= \frac{3}{4} sin^{\frac{4}{3}} (x)

Add a constant to the solution

= \frac{3}{4} sin^{\frac{4}{3}} (x) + C

What is the integral of (sin(x))^{1/3}cos(x) ?
The integral of (sin(x))^{1/3}cos(x) is 3/4 sin^{4/3}(x)+C