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

The integral of 2x^2\sqrt[4]{5x^3+4} is 8/75 (5x^3+4)^{5/4}+C

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

\frac{8}{75} (5 x^{3} + 4)^{\frac{5}{4}} + 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{4}{5} u^{\frac{5}{4}}

= 2 \cdot \frac{1}{15} \cdot \frac{4}{5} u^{\frac{5}{4}}

Substitute back

u = 5 x^{3} + 4

= 2 \cdot \frac{1}{15} \cdot \frac{4}{5} (5 x^{3} + 4)^{\frac{5}{4}}

Simplify

2 \cdot \frac{1}{15} \cdot \frac{4}{5} (5 x^{3} + 4)^{\frac{5}{4}} : \frac{8}{75} (5 x^{3} + 4)^{\frac{5}{4}}

= \frac{8}{75} (5 x^{3} + 4)^{\frac{5}{4}}

Add a constant to the solution

= \frac{8}{75} (5 x^{3} + 4)^{\frac{5}{4}} + C

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What is the integral of 2x^2\sqrt[4]{5x^3+4} ?
The integral of 2x^2\sqrt[4]{5x^3+4} is 8/75 (5x^3+4)^{5/4}+C