Solution assignment 10 Integration of standard functions

Solve:

$\displaystyle\int_{0}^{1}{\displaystyle\frac{x^4+2x^2}{x^2}}dx$

This seems a difficult integral, but the integrand can be written as:

$\displaystyle\frac{x^4+2x^2}{x^2}=\displaystyle\frac{x^4}{x^2}+2\displaystyle\frac{x^2}{x^2}=x^2+2$

and thus the integral becomes:

$\displaystyle\int_{0}^{1}{\displaystyle\frac{x^4+2x^2}{x^2}}dx=[\displaystyle\frac{1}{3}x^3+2x]_{0}^{1}=\displaystyle\frac{7}{3}$