Chapter 8 - Techniques of Integration - 8.1 Integration by Parts - Exercises - Page 396: 71

Use $u= x^2+4x+3\ \ \ \ \to \ \ \ du =2x+4 $

Given $$ \int \frac{x+2}{x^{2}+4 x+3} d x$$ Let $$u= x^2+4x+3\ \ \ \ \to \ \ \ du =2x+4 $$ Then \begin{align*} \int \frac{x+2}{x^{2}+4 x+3} d x&=\int \frac{2du}{u} \\ &=2\ln |u|+C\\ &=2\ln |x^2+4x+3|+C \end{align*}