Q. 32 - Calculus

Question

Integral Formulas: 

Fill in the blanks to complete each of the following integration formulas.

(The last six formulas involve hyperbolic functions and their inverses.)

$\int \frac{1}{x}dx=\_\_\_\_\_\_.$

Step-by-Step Solution

Answer

Ans: $\int \frac{1}{x}dx=\ln \left(\left|x\right|\right)+c$

Step 1. Given information:

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

Step 2. Solution:

$$\begin{gathered} \int \frac{1}{x}dx =\int x^{-1}dx \\ =\ln \left(\left|x\right|\right)+c \end{gathered}$$