∫dxx(x+1)=
log(x+1)(x)+c
log(x)(x+1)+c
log(x-1)(x)+c
log(x–1)(x+1)+c
Explanation for the correct option:
Finding the integral:
Add and subtract x in the numerator.
∫dxx(x+1)
=∫(x+1-x)dxx(x+1)=∫x+1x(x+1)-xx(x+1)dx=∫1x-1(x+1)dx=logx-logx+1+c∵∫1x=logxsimilarly∫1x+1=logx+1=logxx+1+c∵logMN=logM-logN
Hence the correct answer is option (B).