What is the integral of (5x^2-10x)/(\sqrt[4]{3x^3)} ?

The integral of (5x^2-10x)/(\sqrt[4]{3x^3)} is (20)/(9\sqrt[4]{3)}x^{9/4}-8/(\sqrt[4]{3)}x^{5/4}+C

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integral of (5x^2-10x)/(\sqrt[4]{3x^3)}

Solution steps

Apply u-substitution

Take the constant out:

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

Expand

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

\int \frac{2}{u ^{\frac{7}{12}}} d u = \frac{24}{5} u^{\frac{5}{12}}

Substitute back

u = x^{3}

Simplify

Add a constant to the solution

What is the integral of (5x^2-10x)/(\sqrt[4]{3x^3)} ?
The integral of (5x^2-10x)/(\sqrt[4]{3x^3)} is (20)/(9\sqrt[4]{3)}x^{9/4}-8/(\sqrt[4]{3)}x^{5/4}+C