Määritä
a)
[[$\int_{ }^{ }\left(\frac{1}{x^2}+3\sqrt{x}\right)dx\ \ \ \left(molemmat\ muokataan\ muotoon\ x^n\right)$]]
[[$=\int_{ }^{ }\left(x^{-2}+3\cdot x^{\frac{1}{2}}\right)dx=\frac{1}{-1}\cdot x^{-1}+3\cdot\frac{2}{3}x^{\frac{3}{2}}+c$]]
[[$=-\frac{1}{x}+2\sqrt{x^3}+c$]]
[[$Huom!\ kirjan\ vastauksissa\ \sqrt{x^3}\ on\ sievennetty\ muotoon\ x\sqrt{x}\left(=x^{\frac{3}{2}}=x\cdot x^{\frac{1}{2}}\right)$]]

b)
[[$\int_{ }^{ }\frac{3x^3+2x^2-x}{x^2}dx=\int_{ }^{ }\left(\frac{3x^3}{x^2}+\frac{2x^2}{x^2}-\frac{x}{x^2}\right)dx$]]
[[$=\int_{ }^{ }\left(3x+2-\frac{1}{x}\right)dx=3\cdot\frac{1}{2}x^2+2x-\ln\left|x\right|+c$]]