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Integrate the functions(x^2)/(sqrt(x^6+a...

Integrate the functions`(x^2)/(sqrt(x^6+a^6))`

Text Solution

Verified by Experts

Let `I = int(x^2)/(sqrt(x^6+a^6)) dx `
= `1/3int(x^2)/(sqrt((x^3)^2+a^6)) dx `.....(i)
Putting `x^3 = t`
=> `3x^2 = dt/dx`
=> `3x^2 dx= dt`
from equation (i)
`I = 1/3 int(x^2)/(sqrt(t^2+(a^3)^2)) `
...
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