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int((sqrt(x))^5dx)/((sqrt(x))^7+x^6)=lam...

`int((sqrt(x))^5dx)/((sqrt(x))^7+x^6)=lambdalog((x^a)/(x^a+1))+c,` then `a+lambda`

A

`=2`

B

`gt 2`

C

`lt2`

D

`=1`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `I=int((sqrtx)^5)/((sqrtx)^7+x^6)dx = int (dx)/((sqrtx)^2 + (sqrtx)^7)=int(dx)/((sqrtx)^7 (1/(sqrtx)^5 + 1)`
Put `1/((sqrtx)^5)+1=t rArr (dx)/((sqrtx)^7 )=-2/5dt`
`I=-2/5 int(dt)/t=-2/5 ln |t|+c = -2/5 ln |1/(sqrtx)^5+1|+c =2/5 ln ((sqrtx)^5/((sqrtx)^5+1))+c=2/5 ln (x^(5//2)/(x^(5//2) + 1))+c`
On comparing , we get : `lambda=2/5` and `a=5/2 rArr lambda + a > 2`
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