Question

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)`

Answer 1

Correct Answer - 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)`