[tex] \int\limits^1_0 (x^2*{\frac{x}{x+1}}+x^3*\frac{x}{x+1}) \, dx =\int\limits^1_0 {\frac{x}{x+1}(x^2+x^3)} \, dx =\int\limits^1_0 {\frac{x}{x+1}*x^2*(1+x)} \, dx =Se~simplifica~(x+1)~cu~(x+1)~si~x*x^2~este~x^3=\int\limits^1_0 {x^3} \, dx =\frac{x^4}{4}|_0^1=\frac{1}{4} -0=\frac{1}{4} [/tex]
