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

The integral of 4x^2\sqrt[4]{x^3+7} is 16/15 (x^3+7)^{5/4}+C

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

\frac{16}{15} (x^{3} + 7)^{\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

= 4 \cdot \frac{1}{3} \cdot \frac{4}{5} u^{\frac{5}{4}}

Substitute back

u = x^{3} + 7

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

Simplify

4 \cdot \frac{1}{3} \cdot \frac{4}{5} (x^{3} + 7)^{\frac{5}{4}} : \frac{16}{15} (x^{3} + 7)^{\frac{5}{4}}

= \frac{16}{15} (x^{3} + 7)^{\frac{5}{4}}

Add a constant to the solution

= \frac{16}{15} (x^{3} + 7)^{\frac{5}{4}} + C

What is the integral of 4x^2\sqrt[4]{x^3+7} ?
The integral of 4x^2\sqrt[4]{x^3+7} is 16/15 (x^3+7)^{5/4}+C