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int(e^(x//2))/(sqrt(a^2e^x+b^2e^(-x)))dx...

`int(e^(x//2))/(sqrt(a^2e^x+b^2e^(-x)))dx`

A

`(1)/(b)log|e^x-sqrt(e^(2x)+(b^2)/(a^2))|+c`

B

`(1)/(b)log|e^x+sqrt(e^(2x)+(b^2)/(a^2))|+c`

C

`(1)/(a)log|e^x-sqrt(e^(2x)+(b^2)/(a^2))|+c`

D

`(1)/(a)log|e^x+sqrt(e^(2x)+(b^2)/(a^2))|+c`

Text Solution

Verified by Experts

The correct Answer is:
D
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