Enraging Pythagoras 2.0
Calculus
Level
2
True or False?
If \[ \int \frac{e^x}{1+x^2} \ dx = f(x)e^x + C,\] where \(C\) is a constant, then \(f\) is a rational function. That is, \(f(x) = \frac{\mathrm{P}(x)}{\mathrm{Q}(x)},\) where \(\mathrm{P}(x)\) and \(\mathrm{Q}(x)\) are real polynomials in \(x.\)
Note: This problem was adapted from a question in the 2016 STEP III exam.
by
Jake Lai