Solve $\int \frac{1}{x}dx$

Step-by-step solution

1. Step 1 · Why the power rule fails
   $$\int x^{n}dx=\frac{x^{n+1}}{n+1}+C(n\ne -1)$$

   Here n = −1, which would divide by zero, so a separate result is needed.

2. Step 2 · Standard antiderivative
   $$\ln |x|+C$$

   The absolute value covers negative x, where the derivative of ln|x| is still 1/x.