Enraging Pythagoras 2.0

Calculus Level 2

True or False?

If ex1+x2 dx=f(x)ex+C, \int \frac{e^x}{1+x^2} \ dx = f(x)e^x + C, where CC is a constant, then ff is a rational function. That is, f(x)=P(x)Q(x),f(x) = \frac{\mathrm{P}(x)}{\mathrm{Q}(x)}, where P(x)\mathrm{P}(x) and Q(x)\mathrm{Q}(x) are real polynomials in x.x.


Note: This problem was adapted from a question in the 2016 STEP III exam.

×

Problem Loading...

Note Loading...

Set Loading...