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

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

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

\int \frac{4}{3 2 x + 1} d x

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

Solution steps

\int \frac{4}{3 2 x + 1} d x

Take the constant out:

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

= 4 \cdot \int \frac{1}{3 2 x + 1} d x

Apply u-substitution

: \int \frac{1}{2 3 u} d u

= 4 \cdot \int \frac{1}{2 3 u} d u

Take the constant out:

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

= 4 \cdot \frac{1}{2} \cdot \int \frac{1}{3 u} d u

Apply the Power Rule

: \frac{3}{2} u^{\frac{2}{3}}

= 4 \cdot \frac{1}{2} \cdot \frac{3}{2} u^{\frac{2}{3}}

Substitute back

u = 2 x + 1

= 4 \cdot \frac{1}{2} \cdot \frac{3}{2} (2 x + 1)^{\frac{2}{3}}

Simplify

4 \cdot \frac{1}{2} \cdot \frac{3}{2} (2 x + 1)^{\frac{2}{3}} : 3 (2 x + 1)^{\frac{2}{3}}

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

Add a constant to the solution

= 3 (2 x + 1)^{\frac{2}{3}} + C

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