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# Integrate the functions x ^2 / 2 + 3 x^3

Q13  Integrate the functions  $\frac{x ^2 }{(2+3x^3)^3}$

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Given function  $\frac{x ^2 }{(2+3x^3)^3}$,

$\int \frac{x ^2 }{(2+3x^3)^3} dx$

Assume the $2+3x^3 =t$

$\therefore 9x^2dx=dt$

$\implies \int\frac{x^2}{(2+3x^2)}dx = \frac{1}{9}\int \frac{dt}{t^3}$

$= \frac{1}{9}\left ( \frac{t^{-2}}{-2} \right ) +C$

$= \frac{-1}{18}\left ( \frac{1}{t^2} \right )+C$

$= \frac{-1}{18(2+3x^3)^2}+C$  , where C is any constant value.

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