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Find int sqrtx/sqrt(a^3-x^3) dx...

Find `int sqrtx/sqrt(a^3-x^3) dx`

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The correct Answer is:
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Let ` I = int(sqrt(x))/(sqrt(a^(3)-x^(3))) = int(sqrt(x))/(sqrt((a^(3//2))^(2)-(x^(3//2))^(2)))`
Put ` x^(3//2) = t rArr 3/2 x^(1//2) dx = dt`
`:. I = 2/3 int (dt)/(sqrt((a^(3//2))^(2) - t^(2))) = 2/3 sin^(-1) '(t)/(a^(3//2)) +C`
`= 2/3 sin^(-1)'(x^(3//2))/(a^(3//2)) + C = 2/3 sin^(-1) sqrt((x^(3))/(a^(3)))+C`
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