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

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

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

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

Solution steps

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

Apply u-substitution

= \int \frac{1}{4 u} d u

Apply the Power Rule

= \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

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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