Question

Cum calculez integrala din x la puterea 2 supra x+1?

Answer 1

$\int\limits^a_b { \frac{x*x}{x+1} } \, dx = \int\limits^a_b { \frac{x+1}{x+1}*x } \, dx - \int\limits^a_b { \frac{x}{x+1} } \, dx = \frac{x^2}{2} - \int\limits^a_b {1} \, dx + \int\limits^a_b { \frac{1}{x+1} } \, dx = \\ \frac{x^2}{2}- x+ln|x+1|+c$
Daca nu ai inteles ceva, spune-mi.