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The value of the integral int(x^2+x)(x^(...

The value of the integral `int(x^2+x)(x^(-8)+2x^(-9))^(1/(10))dx` is `5/(11)(x^2+2x)^((11)/(10))+c` (b) `5/6(x+1x)^((11)/(10))+c` `6/7(x+1)^((11)/(10))+c` (d) none of these

A

`(5)/(11)(x^(2)+2x)^(11//10)+c`

B

`(5)/(6)(x+1)^(11//10)+c`

C

`(6)/(7)(x+1)^(11//10)+c`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Given that
`I=int(x^(2)+x)(x^(-8)+2x^(-9))^(1//10) dx`
`=int (x+1)(x^(2)+2x)^(1//10)dx`
Now put `x^(2)+2x=t " and "(x+1)dx=(dt)/(2)`
` :. I=int t^(1//10)(dt)/(2)=(1)/(2)xx(10)/(11)t^(11//10)+C=(5)/(11)t^(11//10)+C`
` =(5)/(11)(x^(2)+2x)^(11//10)+C`
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CENGAGE-INDEFINITE INTEGRATION-Exercise (Single)
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  10. If In=int( lnx)^n dx then In+nI(n-1)

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  14. Ifintxlog(1+1/x)dx=f(x)log(x+1)+g(x)x^2+A x+C , then f(x)=1/2x^2 (b) ...

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