Calculus integral question?

Question

What is integration of dx/(x^2 + x) ?

Answer 1

ʃdx/(x^2 + x)

= ʃdx/{x(x + 1)}

= ʃ{1/x - 1/(1+x)}dx

= ʃ(1/x)dx - ʃ1/(1+x)dx

apply farmula ʃ(1/x)dx = log|x| + c

= log|x| - log|1+x| +c

apply log|a| - log|b| = log|a/b|

= log|x/(1+x)|

= log{x/(1+x)}

The sloution is log{x/(1+x)]