What is the integral of x\sqrt[3]{x+10} ?

The integral of x\sqrt[3]{x+10} is 3/7 (x+10)^{7/3}-15/2 (x+10)^{4/3}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x\sqrt[3]{x+10}

\frac{3}{7} (x + 10)^{\frac{7}{3}} - \frac{15}{2} (x + 10)^{\frac{4}{3}} + C

Solution steps

Apply u-substitution

Expand

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

\int u^{\frac{4}{3}} d u = \frac{3}{7} u^{\frac{7}{3}}

= \frac{3}{7} u^{\frac{7}{3}} - \frac{15}{2} u^{\frac{4}{3}}

Substitute back

u = x + 10

= \frac{3}{7} (x + 10)^{\frac{7}{3}} - \frac{15}{2} (x + 10)^{\frac{4}{3}}

Add a constant to the solution

= \frac{3}{7} (x + 10)^{\frac{7}{3}} - \frac{15}{2} (x + 10)^{\frac{4}{3}} + C

\int \frac{x ^{4}}{x ^{2} - 1} d x

\int x cos (x n) d x

\int x (6 - x) d x

\frac{s}{( s ^{2} - k ^{2} )}

\frac{\partial}{\partial x} ((x^{3}) x^{2} + 9)

What is the integral of x\sqrt[3]{x+10} ?
The integral of x\sqrt[3]{x+10} is 3/7 (x+10)^{7/3}-15/2 (x+10)^{4/3}+C