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Question
Integrate the function `x^2/sqrt(x^6 + a^6)`
Solution
Let `I = x^2/sqrt(x^6 + a^6) dx`
`= int x^2/sqrt((x^3)^2 + (a^3)^2) dx`
Put x3 = t
3x2 dx = dt ⇒ x2 dx = `1/3` dt
`therefore I = 1/3 int dt/sqrt(t^2 + (a^3)^2)`
`= 1/3 log [t + sqrt (t^2 + a^6)] + C` `...[∵ int dx/ sqrt(x^2 + a^2) = log |x + sqrt (x^2 + a^2)| + C]`
`= 1/3 log [x^3 + sqrt(x^6 + a^6)] + C`
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