Question

Explain why the formula for the integral of $x^k$does not

apply when$k=-1.$ What is the integral of $x^{-1}?$

Short answer

Integral of $x^k$does not apply when $k=-1$because integral $x^{-1}$of is undefined.

Step-by-step solution

Step 1. Given information. 

The given expression whose integral need to be determine is $x^{-1}.$

Step 2. Explanation.

Integral of $x^{-1}.$

role="math" localid="1648620763103" $\int x^k=\frac{1}{k+1}{x}^{k+1}+C$

Substitute role="math" $k=-1.$

$$\begin{gathered} \int x^{-1}=\frac{1}{-1+1}{x}^{-1+1}+C \\ =\frac{1}{0}{x}^0+C \end{gathered}$$

Since $\frac{1}{0}$is undefined so integral of $x^k$does not apply when $k=-1$because integral of$x^{-1}$is undefined.