Integration of (1+x)/(1+x^2)
Published On :2020-11-11 17:58:00
begin{array}{l} smallint frac{{1 + x}}{{1 + {x^2}}}{rm{d}}x\\ smallint frac{1}{{{x^2} + 1}}dx + smallint frac{x}{{{x^2} + 1}}dx\ By;substitution\ let Rightarrow u = {x^2} + 1\ du = 2xdx\ {tan ^{ - 1}}x + frac{1}{2}smallint frac{1}{u}du\ {tan ^{ - 1}}x + frac{1}{2}ln u + c\ Rightarrow {tan ^{ - 1}}x + frac{1}{2}ln left( {{x^2} + 1} right) + c end{array}