Question

Cum calculez:

∫$\frac{3 x^{2} +2x+1}{x^{2}}dx$ ?

Va multumesc

Answer 1

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