Question

find the ∫\frac{2x}{1+x²} ​

Answer 1

$\tt \int \frac{2x}{1+{x}^{2}} \: dx\\ \\ \tt Substituting \: 1 + {x}^{2} = t \\ \\ \tt \therefore 2x \: dx = dt \\ \\ \tt \therefore \int \frac{1}{t} \:dt \\ \\ \tt \therefore {log}_{e}{t} + c \\ \\ \tt \therefore {log}_{e}{(1+{x}^{2})} + c \\ \\ \tt \therefore \boxed{\bold{\underline{\red{ \int \frac{2x}{1+{x}^{2}} \: dx = {log}_{e}{(1+{x}^{2})} + c }}}}$