What is the integral of sin(12x)\sqrt[3]{cos(12x)} ?

The integral of sin(12x)\sqrt[3]{cos(12x)} is -1/16 cos^{4/3}(12x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of sin(12x)\sqrt[3]{cos(12x)}

- \frac{1}{16} cos^{\frac{4}{3}} (12 x) + C

Solution steps

Apply u-substitution

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

Apply u-substitution

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

Apply the Power Rule

= \frac{1}{12} (- \frac{3}{4} v^{\frac{4}{3}})

Substitute back

= \frac{1}{12} (- \frac{3}{4} cos^{\frac{4}{3}} (12 x))

Simplify

\frac{1}{12} (- \frac{3}{4} cos^{\frac{4}{3}} (12 x)) : - \frac{1}{16} cos^{\frac{4}{3}} (12 x)

= - \frac{1}{16} cos^{\frac{4}{3}} (12 x)

Add a constant to the solution

= - \frac{1}{16} cos^{\frac{4}{3}} (12 x) + C

What is the integral of sin(12x)\sqrt[3]{cos(12x)} ?
The integral of sin(12x)\sqrt[3]{cos(12x)} is -1/16 cos^{4/3}(12x)+C