What is the integral of (2x+1)/(\sqrt[4]{x^2+x)} ?

The integral of (2x+1)/(\sqrt[4]{x^2+x)} is 4/3 (x^2+x)^{3/4}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x+1)/(\sqrt[4]{x^2+x)}

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

Solution steps

Apply u-substitution

Apply the Power Rule

: \frac{4}{3} u^{\frac{3}{4}}

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

Substitute back

u = x^{2} + x

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

Add a constant to the solution

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

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

\int \frac{7}{5 x 25 x ^{2} - 7} d x

\int 3 cot^{3} (x) csc (x) d x

\int \frac{3 x ^{2} + 7 x - 5}{3 x + 2} d x

\int \frac{1}{tan ( x ) ( 3 - 2 ln ( sin ( x ) ) )} d x

What is the integral of (2x+1)/(\sqrt[4]{x^2+x)} ?
The integral of (2x+1)/(\sqrt[4]{x^2+x)} is 4/3 (x^2+x)^{3/4}+C