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Let I(1)=int(0)^(oo)(x^(2)sqrtx)/((1+x)^...

Let `I_(1)=int_(0)^(oo)(x^(2)sqrtx)/((1+x)^(6))dx,I_(2)=int_(0)^(oo)(xsqrtx)/((1+x)^(6))dx`, then

A

`I_(1)=2I_(2)`

B

`I_(2)=2I_(1)`

C

`I_(1)=I_(2)`

D

`I_(1)=-I_(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`I_(1)=int_(0)^(oo)(x^(2)sqrtx)/((1+x)^(6))dx`
Let `x=(1)/(t)`
`rArr" "I_(1)=int_(oo)^(0)((1)/(t^(2)sqrtt))/((1+(1)/(t))^(6))(-(1)/(t^(2))dt)`
`rArr" "I_(1)=int_(0)^(oo)(tsqrtt)/((1+t)^(6))dt=I_(2)`
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