Question

integrate ( (2x+1).(x^2+x+1)dx ) / ( (x^2+x+1)^2 + (x^2+x+1) )
@MIT 18.01 Single …

Answer 1

Divide top and bottom by x^2+x+1 to give:
\[(2x+1)/x ^{2}+x+2\]
Use substitution
\[u=x^2+x+2\]which means that
\[du=(2x+1)dx\]Hence the integral becomes
\[\int\limits_{}^{}(1/u)du\]which is
\[\ln|u| + C = \ln|x^2+x+2| + C\]