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int(x^(e-1)+e^(x-1))/(x^(2)+e^(x)) dx is...

`int(x^(e-1)+e^(x-1))/(x^(2)+e^(x))` dx is equal to

A

`log(x^(e)+e^(x))+C`

B

`e log(x^(e)+e^(x))+C`

C

`(1)/(e)log.(x^(e)+e^(x))+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Put `x^(e)+e^(x)=t rArr e(x^(e-1)+e^(x-1))dx=dt`
`therefore" "int(x^(e-1)+e^(x-1))/(x^(e)+e^(x))dx=(1)/(2)int(dt)/(t)=(1)/(e)log t +C`
`=(1)/(e)log(x^(e)+e^(x))+C`
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