$\int\left(\frac{20}{100x^2+1}\right)dx$

$5xy-1=0$

$\frac{dy}{dx}=\left(1-x\right)\left(y+1\right)$

$\frac{\left(u-1\right)\left(1\right)-\left(u+1\right)\left(1\right)}{\left(u-1\right)^2}$

$\frac{dy}{dx}=\left(y-1\right)\left(y-4\right)^2\left(y-7\right)^2\left(y-8\right)$

$\int_0^r\frac{r}{\sqrt{r^2-x^2}}dx$

$\frac{3y}{x}+3$