Question

integral de x²/x²+1 dx

Answer 1

$\displaystyle\int \!\dfrac{x^2}{x^2+1}\,dx\\\\\\ =\int \!\dfrac{x^2+1-1}{x^2+1}\,dx\\\\\\ =\int \!\left(\dfrac{x^2+1}{x^2+1}-\dfrac{1}{x^2+1}\right)dx\\\\\\ =\int \!\left(1-\dfrac{1}{x^2+1}\right)dx\\\\\\ =\int \!dx-\int\!\dfrac{1}{1+x^2}\,dx$

$=x-\mathrm{arctg\,}x+C$


Bons estudos! :-)