Integral taken from instagram user @integralsforyou

$$\int\frac{x^2+a}{x^2+b^2}dx$$

$$=\int(\frac{x^2+b^2}{x^2+b^2}+\frac{a-b^2}{x^2+b^2})dx$$

$$=\int(1)dx+(a-b^2)\int\frac{1}{b^2+x^2}dx$$

$$=x+(\frac{a-b^2}{b})\arctan(\frac{x}{b})+C$$