Question

integration of [x³ + 5x² - 4]/x² . dx

Answer 1

$\bf{I=\int{\frac{x^3+5x^2-4}{x^2}}\,dx}\\\\=\bf{\int{\frac{x^3}{x^2}}\,dx+5\int{\frac{x^2}{x^2}}\,dx-4\int{\frac{1}{x^2}}\,dx}\\\\=\bf{\int{x}\,dx+5\int{dx}-4\int{x^{-2}}\,dx}\\\\=\bf{\frac{x^2}{2}+5x-4\frac{x^{-2+1}}{-2+1}+C}\\\\=\bf{\frac{x^2}{2}+5x+\frac{4}{x}+C}$

hence, I = x²/2 + 5x + 4/x + C