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Evaluate: int(x^(5/2))/(sqrt(1+x^7))dx...

Evaluate: `int(x^(5/2))/(sqrt(1+x^7))dx`

A

`(2)/(7)log|x^(7//2)+sqrt(1+x^(7))|+C`

B

`(1)/(2)log|(x^(7)+1)/(x^(7)-1)|+C`

C

`2sqrt(1+x^(7))+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
a
Let `=int(x^(5//5))/(sqrt(1+x^(7)))dx`
`rArrI=(2)/(7)int(1)/(sqrt(1^(2)+(x^(7//2))^(2))^(7/(2)x(5)/(2)))dx`
`rArrI=(2)/(7)int(1)/(sqrt(1^(2)+(x^(7//2))^(2)))d(x^(7//2))=(2)/(7)log|x^(7//2)+sqrt(1+x^(7))|+C`
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