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)
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
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Correct Answer - 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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