Question

y=x / (x^2 +1) найти первообразную

Answer 1

$Y(x)=\int{\frac{x}{x^2+1}}\, dx=\frac{1}{2}\int{\frac{2x}{x^2+1}}\, dx=\\ \frac{1}{2}\int{\frac{1}{x^2+1}}\, d(x^2+1)=\frac{1}{2}ln|x^2+1|+c=ln \sqrt{x^2+1}+c$

 

c є R