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If int((1-x^7))/(x(1+x^7))dx=Plogabsx+Ql...

If `int((1-x^7))/(x(1+x^7))dx=Plogabsx+Qlogabs(x^7+1)+c`

A

`a=1`

B

`a= -1`

C

`b=(2)/(7)`

D

`b= -(2)/(7)`

Text Solution

Verified by Experts

The correct Answer is:
A, D
`I=int(1-x^(7))/(x(1+x^(7)))dx=a log_(e)|x|+b log_(e)|1+x^(7)|+c`
Differentiating both sides w.r.t. x, we get
`(1-x^(7))/(x(1+x^(7)))=(a)/(x)+b.(7x^(6))/(1+x^(7))`
`implies1-x^(7)=a(1+x^(7))+7bx^(7)`
`impliesa=1, a+7b= -1`
`implies b= -2//7`
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