Q. 49 - Calculus

Question

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

$\int \frac{1}{1-x^2}dx=...$. 

Step-by-Step Solution

Answer

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

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 ∫ 1 1 - x 2 d x .

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