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True or False?
If ∫ex1+x2 dx=f(x)ex+C, \int \frac{e^x}{1+x^2} \ dx = f(x)e^x + C,∫1+x2ex dx=f(x)ex+C, where CCC is a constant, then fff is a rational function. That is, f(x)=P(x)Q(x),f(x) = \frac{\mathrm{P}(x)}{\mathrm{Q}(x)},f(x)=Q(x)P(x), where P(x)\mathrm{P}(x)P(x) and Q(x)\mathrm{Q}(x)Q(x) are real polynomials in x.x.x.
Note: This problem was adapted from a question in the 2016 STEP III exam.
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