What is the integral of (-2x)/(\sqrt[4]{x+2)} ?

The integral of (-2x)/(\sqrt[4]{x+2)} is -2(4/7 (x+2)^{7/4}-8/3 (x+2)^{3/4})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (-2x)/(\sqrt[4]{x+2)}

- 2 (\frac{4}{7} (x + 2)^{\frac{7}{4}} - \frac{8}{3} (x + 2)^{\frac{3}{4}}) + C

Solution steps

Take the constant out:

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

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

= - 2 (\frac{4}{7} u^{\frac{7}{4}} - \frac{8}{3} u^{\frac{3}{4}})

Substitute back

u = x + 2

= - 2 (\frac{4}{7} (x + 2)^{\frac{7}{4}} - \frac{8}{3} (x + 2)^{\frac{3}{4}})

Add a constant to the solution

= - 2 (\frac{4}{7} (x + 2)^{\frac{7}{4}} - \frac{8}{3} (x + 2)^{\frac{3}{4}}) + C

What is the integral of (-2x)/(\sqrt[4]{x+2)} ?
The integral of (-2x)/(\sqrt[4]{x+2)} is -2(4/7 (x+2)^{7/4}-8/3 (x+2)^{3/4})+C