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int1/(sqrt(x+a)+sqrt(x+b))\ dx...

`int1/(sqrt(x+a)+sqrt(x+b))\ dx`

A

`(2)/(5(a-b))((x+a)^((5)/(2))+(x+b)^((5)/(2)))-(2)/(3(a-b))((x+b)^((3)/(2))+(x+a)^((3)/(2)))+c`

B

`(2)/(5(a-b))((x+a)^((5)/(2))+(x+b)^((5)/(2)))+(2)/(3(a-b))((x+b)^((3)/(2))+(x+a)^((3)/(2)))+c`

C

`(2)/(5(a-b))((x+a)^((5)/(2))-(x+b)^((5)/(2)))-(2)/(3(a-b))(b(x+b)^((3)/(2))-(x+a)^((3)/(2)))+c`

D

`(2)/(5(a-b))((x+a)^((5)/(2))-(x+b)^((5)/(2)))+(2)/(3(a-b))(b(x+b)^((3)/(2))-a(x+a)^((3)/(2)))+c`

Text Solution

Verified by Experts

The correct Answer is:
D
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