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int(1-x^(7))/(x(1+x^(7)))dx equals...

`int(1-x^(7))/(x(1+x^(7)))dx` equals

A

`a=1,b=(2)/(7)`

B

`a=-1,b=(2)/(7)`

C

`a=1,b=-(2)/(7)`

D

`a=-1,b=-(2)/(7)`

Text Solution

Verified by Experts

The correct Answer is:
c
We have , `int(1-x^(7))/(x(1+x^(7)))dx=aIn |x| +bIn|x^(7)+1|+C`
Differentiating both sides W.r.t to , x, to x, we get
`(1-x^(7))/(x(1+x^(7)))=(a)/(x)+7b(x^(6))/(x^(7)+1)`
`rArr1-x^(7)=a(1+x^(7))+7bx^(7)rArra=1,b=-(2)/(7)`
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