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Evaluate: int(x^(3/2))/(sqrt(1+x^5))dx...

Evaluate: `int(x^(3/2))/(sqrt(1+x^5))dx`

Text Solution

Verified by Experts

The correct Answer is:
`(2)/(7)log(x^(7//2)+sqrt(1+x^(7)))+C`
` "Put "x^(7//2)=t`
` :. (7)/(2)x^(5//2)dx=dt`
` :. I=int(2)/(7)(dt)/(sqrt(1+t^(2)))=(2)/(7)log(t+sqrt(1+t^(2)))+C`
`=(2)/(7)log(x^(7//2)+sqrt(1+x^(7)))+C`
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