What is the integral of x^2\sqrt[3]{x} ?

The integral of x^2\sqrt[3]{x} is 1/3 x^3\sqrt[3]{x}-1/30 x^{10/3}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x^2\sqrt[3]{x}

\int x^{2} 3 x d x

\frac{1}{3} x^{3} 3 x - \frac{1}{30} x^{\frac{10}{3}} + C

Solution steps

\int x^{2} 3 x d x

Apply Integration By Parts

= \frac{1}{3} x^{3} 3 x - \int \frac{1}{9} x^{\frac{7}{3}} d x

\int \frac{1}{9} x^{\frac{7}{3}} d x = \frac{1}{30} x^{\frac{10}{3}}

= \frac{1}{3} x^{3} 3 x - \frac{1}{30} x^{\frac{10}{3}}

Add a constant to the solution

= \frac{1}{3} x^{3} 3 x - \frac{1}{30} x^{\frac{10}{3}} + C

\int \frac{cos ( 2 x )}{sin ( x ) + cos ( x )} d x

\int y cos (5 y) d y

\int 3 - 2 x^{2} d x

\int \frac{x ^{3}}{( 1 + x ^{8} ) ^{2}} d x

\int \frac{3}{x ( ln ( x ) ) ^{4}} d x

What is the integral of x^2\sqrt[3]{x} ?
The integral of x^2\sqrt[3]{x} is 1/3 x^3\sqrt[3]{x}-1/30 x^{10/3}+C