Chapter 8.2, Problem 76E

Find the error Suppose you evaluate ${\displaystyle \int \frac{dx}{x}}$ using integration by parts. With u = 1/x and dv = dx, you find that du = −1/x² dx, v = x, and

${\displaystyle \int \frac{dx}{x}=\left(\frac{1}{x}\right)x-{\displaystyle \int x\left(-\frac{1}{x^2}\right)}dx=1+{\displaystyle \int \frac{dx}{x}.}}$

You conclude that ü = 1. Explain the problem with the calculation.