Question

интеграл (x^2+1)/(x+1) dx

Answer 1

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