Problem

f) $\int \sqrt[3]{3 x^{3} - 5 x^{5}} d x$

Answer

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Answer

$\int \sqrt[3]{u (x)} \frac{d u (x)}{d x} d x = \int u^{\frac{1}{3}} d u$

Steps

Step 1 ： $u (x) = 3 x^{3} - 5 x^{5}$

Step 2 ： $\frac{d u (x)}{d x} = 9 x^{2} - 25 x^{4}$

Step 3 ： $\int \sqrt[3]{u (x)} \frac{d u (x)}{d x} d x = \int u^{\frac{1}{3}} d u$

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