∫x51+x323dx is equal to - Infinity Learn by Sri Chaitanya

A
$\frac{1}{8} u^{8 / 3} - \frac{1}{5} u^{5 / 3} + C, u = 1 + x^{3}$
B
$\frac{3}{8} u^{8 / 3} - \frac{3}{5} u^{5 / 3} + C, u = 1 + x^{3}$
C
$- \frac{3}{8} u^{8 / 3} + \frac{3}{5} u^{5 / 3} + C, u = 1 + x^{3}$
D
$- \frac{1}{8} u^{8 / 3} + \frac{1}{5} u^{5 / 3} + C, u - 1 + x^{3}$

Solution:

Put $1 + x^{3} = t^{3} \Rightarrow x^{2} d x = t^{2} d t$

$\int x^{5} \sqrt[3]{{(1 + x^{3})}^{2}} d x = \int (t^{3} - 1) t^{4} d t$

$\begin{array}{l} = \frac{t^{8}}{8} - \frac{t^{5}}{5} + C \\ = \frac{1}{8} {(1 + x^{3})}^{8 / 3} - \frac{1}{5} {(1 + x^{3})}^{5 / 3} + C . \end{array}$

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$\int x^{5} \sqrt[3]{{(1 + x^{3})}^{2}} d x$ is equal to

Solution:

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