Aloha :)
$$\int\frac{x^2+2x}{x^5}\,dx=\int\left(\frac{x^2}{x^5}+\frac{2x}{x^5}\right)\,dx=\int\left(x^{-3}+2x^{-4}\right)\,dx=\frac{x^{-2}}{-2}+\frac{2x^{-3}}{-3}+c$$$$\phantom{\int\frac{x^2+2x}{x^5}\,dx}=\frac{-3x}{6x^3}+\frac{-4}{6x^3}+c=-\frac{3x+4}{6x^2}+c$$
$$\int\frac{x(x+1)}{x^4}\,dx=\int\left(\frac{x^2}{x^4}+\frac{x}{x^4}\right)\,dx=\int\left(x^{-2}+x^{-3}\right)\,dx=\frac{x^{-1}}{-1}+\frac{x^{-2}}{-2}+c$$$$\phantom{\int\frac{x(x+1)}{x^4}\,dx}=\frac{-2x}{2x^2}+\frac{-1}{2x^2}+c=-\frac{2x+1}{2x^2}+c$$
$$\int\frac{6x^2-21x}{3x^7}\,dx=\int\left(\frac{6x^2}{3x^7}-\frac{21x}{3x^7}\right)\,dx=\int\left(2x^{-5}+7x^{-6}\right)\,dx=\frac{2x^{-4}}{-4}+\frac{7x^{-5}}{-5}+c$$$$\phantom{\int\frac{6x^2-21x}{3x^7}\,dx}=\frac{-10x}{20x^5}+\frac{-28}{20x^5}+c=-\frac{10x+28}{20x^5}+c=-\frac{5x+14}{10x^5}+c$$
