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

Short answer

$\int \frac{1}{\sqrt{x^2-1}}dx=\ln \left|\sqrt{x^2-1}+x\right|+C$

Step-by-step solution

Step 1. Given Information

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

Step 2. Solving the expression

From the formula of integration
$\int \frac{1}{\sqrt{x^2-1}}dx=\ln \left|\sqrt{x^2-1}+x\right|+C$

Where $C$is the constant

So,
$\int \frac{1}{\sqrt{x^2-1}}dx=\ln \left|\sqrt{x^2-1}+x\right|+C$