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

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

\frac{3}{7} (x - 2)^{\frac{7}{3}} + \frac{3}{2} (x - 2)^{\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{3}{2} u^{\frac{4}{3}}

Substitute back

u = x - 2

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

Add a constant to the solution

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

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

x \to - \frac{1}{2} lim (\frac{( 6 x - 1 )}{x})

1 7^{x}

\frac{d}{d x} (π - x)

\frac{x}{x + 2}

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