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int(x^(2)+x)(x^(-8)+2x^(-9))^(1//10)dx i...

`int(x^(2)+x)(x^(-8)+2x^(-9))^(1//10)dx` is equal to

A

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

B

`(5)/(11)(x+1)^(11//10)+C`

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
Let `I=int(x^(2)+x)(x^(-8)+2x^(-9))^(1//10)dx` . then ,
`I=int(x+1)(x^(2)+2x)^(1//10)dx =(1)/(2)int(x^(2)+2x)^(1//10)d(x^(2)+2x)`
`rArrI=(1)/(2)xx((x^(2)+2x)^(11//10))/(11//10)+C=(5)/(11)(x^(2)+2x)^(11//10)+C`
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OBJECTIVE RD SHARMA-INDEFINITE INTEGRALS-Solved Example
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