Let u = 5x+1. Then du = 5·dx, and your integral is
[tex] \displaystyle\frac{1}{5}\int{\frac{5}{5x+1}}\, dx=\frac{1}{5}\int{\frac{1}{u}} \, du}\\\\ =\frac{1}{5}\ln(u)=\frac{1}{5}\ln(5x+1) [/tex]
