Найти интеграл: (1+2х)^2/ x^3 dx

[latex]\int{\frac{(1+2x)^2}{x^3}}dx=\int{\frac{1+4x+4x^2}{x^3}}dx=\\ =\int{\left(\frac1{x^3}+\frac{4}{x^2}+\frac4x\right)}dx=\\ =\int{\left(x^{-3}+4x^{-2}+4x^{-1}\right)}dx=\\ =\int{x^{-3}}dx+4\int{x^{-2}}dx+4\int{\frac1x}dx=\\ =\frac{1}{-3+1}x^{-3+1}+4\cdot\frac1{-2+1}x^{-2+1}+4\ln|x|+C=\\ =-\frac{1}{2x^2}-\frac4x+4\ln|x|+C[/latex]