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Question
Integrate the function:
`x^3/(sqrt(1-x^8)`
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Solution
Let `I = x^3/(sqrt(1 - x^8))` dx
`= 1/4 int (4x^3)/(sqrt (1 - (x^4)^2))`
On substituting x4 = t
4x3 dx = dt
⇒ `x^3 = 1/4 dt`
Hence, `I = 1/4 int dt/sqrt(1 - t^2)`
`= 1/4 sin^-1 t + C`
`= 1/4 sin^-1 (x^4) + C`
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