Question

∫((x^3+1)/(x^2-x))dx найти интеграл

Answer 1

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