Question

Calcule a integral indefinida ∫ x - 3/x2 - 3x + 2 dx usando o método das frações parciais.

Answer 1

$\int\limits{ \frac{x-3}{ x^{2} } } \, dx - \int\limits {3x+2} \, dx$

$\int\limits { \frac{x-3}{x^2} } \, dx = \int\limits { \frac{x}{x^2} } \, dx - \int\limits { \frac{3}{x^2} } \, dx$

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

$\int\limits { \frac{3}{x^2} } \, dx = 3\int\limits { x^{-2} } \, dx = \frac{-3}{x}$

$\int\limits {3x+2} \, dx = \frac{3}{2} x^{2} + 2x$

$= \frac{3}{x} + ln(x) - \frac{3 x^{2} }{2} + 2x + k$