INTEGRAL (1/x) dx = (1/x)*x - INTEGRAL x (-1/x^{2}) dx
= 1 + INTEGRAL (1/x) dx

which implies that 0 = 1.

What's wrong with this calculation?

The Math Behind the Fact:
This is common mistake using integration by parts in calculus.
Students often forget about the constant of integration
for indefinite integrals. In this case, the constants
on both sides will differ by 1.

How to Cite this Page:
Su, Francis E., et al. "One Equals Zero: Integral Form."
Math Fun Facts.
<http://www.math.hmc.edu/funfacts>.

Keywords: calculus, false proof, paradox
Subjects: calculus, analysis, other
Level: Easy
Fun Fact suggested by: James Baglama
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