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Evaluate int(-oo)^(0)(te^(t))/(sqrt(1-e^...

Evaluate `int_(-oo)^(0)(te^(t))/(sqrt(1-e^(2t)))dt`

Text Solution

Verified by Experts

The correct Answer is:
`-(pi)/2log_(e)2`
`I=int_(-oo)^(0)(te^(t))/(sqrt(1-e^(2t)))dt`
Put `e^(t)=x`
`:.I=int_(0)^(1)(log_(e)x)/(sqrt(1-x^(2)))dx`
Put `x=sin theta`
`:. I=int_(0)^(pi//2) log_(e)sin theta d theta =(pi)/2 "log"_(e)1/2`
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