Question

Calcule a seguinte integral indefinida:

∫$\frac{2x^3}{x^2+x}$dx

Answer 1

$\int\limits { \frac{2x^3}{x^2+x} } \, dx \\ \\ 2\int\limits { \frac{x^3}{x(x+1)} } \, dx \\ \\ 2\int\limits { \frac{x^2}{x+1} } \, dx \\ \\ 2\int\limits {(x+ \frac{1}{x+1} -1)} \, dx \\ \\ 2( \frac{x^2}{2} +ln(x+1)-x)+C \\ \\ \boxed{x^2+2ln(x+1)-2x+C}$