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int(dx)/((1+sqrtx)^(2010))=2[(1)/(alpha(...

`int(dx)/((1+sqrtx)^(2010))=2[(1)/(alpha(1+sqrtx)^(alpha))-(1)/(beta(1+sqrtx))^(beta)]+c` where `alpha, betagt0" then "alpha-beta` is

A

1

B

2

C

`-1`

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
A
`int(dx)/((1+sqrtx)^(2010))`
`=int(sqrtx)/(sqrtx(1+sqrtx)^(2010))dx`
`=2int(t-1)/((t-1)(t^(2010)))dt(t=1+sqrtx)`
`=2[(1)/(2009t^(2009))-(1)/(2008t^(2008))]+c`
`rArr" "alpha=2009, beta=2008`
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