Question

Determine a solução para f xdx/4+3x^2

Answer 1

$\int\limits {\dfrac{x}{4+3x^2}} \, dx \\\\\\u=4+3x^2\to \dfrac{du}{dx}=6x\to dx=\dfrac{du}{6x}\\\\\\\int\limits {\dfrac{x}{u}} \, \dfrac{du}{6x}=\\\\\\\int\limits {\dfrac{1}{6u}} \, du =\\\\\\ \dfrac16\int\limits {\dfrac{1}{u}} \, du =\\\\\\\dfrac16\ln u+C=\\\\\\\boxed{\dfrac16\ln (4+3x^2)+C}$