Integration problem 1

April 8, 2021 By Xander Integrals

Integral taken from instagram user @integralsforyou

Python \int\frac{x^2+a}{x^2+b^2}dx 1 \int\frac{x^2+a}{x^2+b^2}dx

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

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

Python =x+(\frac{a-b^2}{b})\arctan(\frac{x}{b})+C 1 =x+(\frac{a-b^2}{b})\arctan(\frac{x}{b})+C