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Integrate the following functions x^2/(2...

Integrate the following functions `x^2/(2+3x^3)^3`

Text Solution

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Let t = `2+3x^3`,
Then dt = `9x^2 dx gt x^2 dx = 1/9 dt`
therefore `int x^2/(2+3x^3)^3 dx = int 1/t^3 1/9 dt`
=`1/9 int r^(-3) dt = 1/9 xx t^(-3+1)/(-3+1) +c`
`1/(-18) t^(-2) +c = -1/(18t^2) +c`
=`-1/(18(2+3x^3)^2 +c`.
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