when you want to use complex numbers to integrate 1/(x^2+1)

Learn more complex numbers by visiting Brilliant 👉 (20% off with this link!) When you want to use complex numbers to integrate 1/(x^2 1)! We didn’t use partial fraction decomposition with complex numbers to integrate 1/(x^2 1) in calculus 2. We usually use a trigonometric substitution to integrate 1/(1 x^2), i.e. the tangent substitution. But here the key is to simplify the complex logarithms and get their principal branch. Be sure to look at the polar form of the complex numbers. Then we can integrate 1/(1 x^2) and get arctan(x), just as expected! This is definitely a great challenge question for any calculus student! 🛍 Get an Euler’s Identity t-shirt: 10% off with the code “WELCOME10“ ---------------------------------------- ***Thanks to ALL my lovely patrons for supporting my channel and believing in what I do*** A