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The value of the integral int0^(log5)(e^...

The value of the integral `int_0^(log5)(e^xsqrt(e^x-1))/(e^x+3)dx`

A

`3+2pi`

B

`4-pi`

C

`2+pi`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Put `e^(x) - 1 = t^(2) rArr e^(x) dx = 2t dt `
Also, as x = 0 to log 5 , t = 0 to 2
` :. int _(0)^(log5) (e^(x) sqrt(e^(x)-1))/(e^(x) +3) dx = int _(0)^(2) (2t^(2))/(t^(2) +4 ) dt `
` = 2 [ int _(0)^(2) 1dt - 4 int_(0)^(2) (dt)/(t^(2)+4)] = 4 - pi`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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