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Question
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Solution
Let `I = int x^2/(2 + 3x^3)^3` dx
Put 2 + 3x3 = t
9x2 dx = dt
or x2 dx `= 1/9` dt
∴ `I = 1/9 int dt/t^3 = 1/9 int t^-3 dt`
`= 1/9 t^-2/(-2) + C = -1/18 t^-2 + C`
`= -1/ (18(2 + 3x^3)^2) + C`
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