What is the integral of (5x\sqrt[3]{5x^2+3})/3 ?

The integral of (5x\sqrt[3]{5x^2+3})/3 is 1/8 (5x^2+3)^{4/3}+C

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integral of (5x\sqrt[3]{5x^2+3})/3

\frac{1}{8} (5 x^{2} + 3)^{\frac{4}{3}} + C

Solution steps

Take the constant out:

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

Apply u-substitution

Take the constant out:

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

Apply u-substitution

Take the constant out:

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

Apply the Power Rule

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

= \frac{5}{3} \cdot \frac{1}{2} \cdot \frac{1}{5} \cdot \frac{3}{4} v^{\frac{4}{3}}

Substitute back

= \frac{5}{3} \cdot \frac{1}{2} \cdot \frac{1}{5} \cdot \frac{3}{4} (5 x^{2} + 3)^{\frac{4}{3}}

Simplify

\frac{5}{3} \cdot \frac{1}{2} \cdot \frac{1}{5} \cdot \frac{3}{4} (5 x^{2} + 3)^{\frac{4}{3}} : \frac{1}{8} (5 x^{2} + 3)^{\frac{4}{3}}

= \frac{1}{8} (5 x^{2} + 3)^{\frac{4}{3}}

Add a constant to the solution

= \frac{1}{8} (5 x^{2} + 3)^{\frac{4}{3}} + C

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What is the integral of (5x\sqrt[3]{5x^2+3})/3 ?
The integral of (5x\sqrt[3]{5x^2+3})/3 is 1/8 (5x^2+3)^{4/3}+C