Evaluate:`int(x^2)/(sqrt(1-x^6))dx`

1.	Evaluate:`int(x^2)/(sqrt(1-x^6))dx`
Answer» Putting `x^(3)= t and x^(2) dx = (1)/(3)dt` , we get `int(x^(2))/(sqrt(x^(6)-1))dx=(1)/(3)int(dt)/(sqrt(t^(2)-1))=(1)/(3)log\|t+sqrt(t^(2)-1)\|+C` `=(1)/(3)log\|x^(3)+sqrt(x^(6)-1)\|+C`.

Discussion

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