5.5 The Substitution Rule/43

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} \int\frac{1+x}{1+x^2}dx &=\int(\frac{1}{1+x^2}+\frac{x}{1+x^2})dx\\[2ex]&=\int\frac{1}{1+x^2}dx+\int\frac{x}{1+x^2}dx\\[2ex]&=tan^{-1}(x) + \frac{1}{2}\int\frac{1}{u}du\\[2ex]&= tan^{-1}(x)+\ln|{1+x}|+c \end{align}}