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Question
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Solution
Let I = `int x^2/sqrt(9 - x^6).dx`
Put x3 = t
∴ 3x2 dx = dt
∴ x2dx = `(1)/(3)dt`
∴ I = `int 1/sqrt(9 - t^2).dt/(3)`
= `(1)/(3) int dt/sqrt(3^2 - t^2)`
= `(1)/(3) sin^-1(t/3) + c`
= `(1)/(3)sin^-1(x^3/3) + c`.
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