1.

If underset(0)overset(oo)(f)(dx)/((x+sqrt(1+x^(2)))^(5))=(m)/(n)where m and relatively prime prime, then the value of (m+n) is

Answer»

31
30
29
28

Solution :Let `x+sqrt(1+x^(2))=t`
`+x^(2)=t^(2)+x^(2)-2txrArr1=t^(2)-2txrArrx=(1)/(2)(t-(1)/(t))rArrdx=(1)/(2)(1+(1)/(t^(2)))dt`
Now,`OVERSET(oo)underset(1)(f)(1)/(t^(5))(1)/(2)(1+(t)/(t^(2)))dt=(1)/(2)overset(oo)underset(1)(f)((1)/(t^(5))+(1)/(t^(4)))dt`
`I=(-1)/(2)((1)/(4T^(4))+(1)/(6t^(6)))underset(1)overset(oo)| `
`I=(5)/(24)=(m)/(n)` (given)
So,(m+n)=29.


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