What is the integral of 2x^3\sqrt[5]{3x^4+7} ?

The integral of 2x^3\sqrt[5]{3x^4+7} is 5/36 (3x^4+7)^{6/5}+C

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integral of 2x^3\sqrt[5]{3x^4+7}

\frac{5}{36} (3 x^{4} + 7)^{\frac{6}{5}} + 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 the Power Rule

: \frac{5}{6} u^{\frac{6}{5}}

= 2 \cdot \frac{1}{12} \cdot \frac{5}{6} u^{\frac{6}{5}}

Substitute back

u = 3 x^{4} + 7

= 2 \cdot \frac{1}{12} \cdot \frac{5}{6} (3 x^{4} + 7)^{\frac{6}{5}}

Simplify

2 \cdot \frac{1}{12} \cdot \frac{5}{6} (3 x^{4} + 7)^{\frac{6}{5}} : \frac{5}{36} (3 x^{4} + 7)^{\frac{6}{5}}

= \frac{5}{36} (3 x^{4} + 7)^{\frac{6}{5}}

Add a constant to the solution

= \frac{5}{36} (3 x^{4} + 7)^{\frac{6}{5}} + C

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What is the integral of 2x^3\sqrt[5]{3x^4+7} ?
The integral of 2x^3\sqrt[5]{3x^4+7} is 5/36 (3x^4+7)^{6/5}+C