How do you integrate $\int \frac{x^{2}}{{(1 + x^{3})}^{2}}$ $intx^2/(1+x^3)^2$ using substitution?

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Answer 1 · 2016-07-20T16:56:24

$= C - \frac{1}{3 (1 + x^{3})}$ $=C -1/(3(1+x^3))$

$u = 1 + x^{3} \Rightarrow d u = 3 x^{2} d x$ $u = 1+x^3 implies du = 3x^2dx$

$therefore 1/3du = x^2dx$

Integral becomes

$1/3int (du)/u^2 = -1/(3u) +C$

$=C -1/(3(1+x^3))$

How do you integrate intx^2/(1+x^3)^2∫x2(1+x3)2intx^2/(1+x^3)^2 using substitution?