Question

Could I (x+1)/(x+2) dx (where I = the integral) be solved as I(x+1)dx - I (x+2)dx?

Answer 1

\[\int \frac{x+1}{x+2}dx\neq \int(x+1)dx-\int(x+2)dx\] no

Answer 2

you can use a nice trick though and write
\[\frac{x+1}{x+2}=\frac{x+2-1}{x+2}=1-\frac{1}{x+2}\] then get
\[\int\frac{x+1}{x+2}dx=\int 1dx-\int\frac{dx}{x+2}\]