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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!
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