Question

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

$\int \frac{1}{1-x^2}dx=...$.

Short answer

The value of$\int \frac{1}{1-x^2}dx={\tanh }^{-1}x+\mathrm{C}$.

Step-by-step solution

Step 1. Given information.

Consider the given integral function$\int \frac{1}{1-x^2}dx$.

Step 2. Fill the blank for the integral function ∫11-x2dx. 

The theorem of Integrals of Hyperbolic Functions states that $\int \frac{1}{1-x^2}dx={\tanh }^{-1}x+\mathrm{C}$.

Therefore, it can be said the appropriate fill in black will be$\int \frac{1}{1-x^2}dx={\tanh }^{-1}x+\mathrm{C}$.