cleritere39

2021-11-07

Use a table of integrals to evaluate the following indefinite integral.

$\int \frac{dx}{\sqrt{{x}^{2}-25}}$

Louise Eldridge

Beginner2021-11-08Added 17 answers

Step 1:To determine

Evaluate:

$\int \frac{dx}{\sqrt{{x}^{2}-25}}$

Step 2:Formula used

$\int \frac{dx}{\sqrt{{x}^{2}-{a}^{2}}}=\mathrm{ln}|x+\sqrt{{x}^{2}-{a}^{2}}|+C$

Step 3:Calculation

Consider the given integral$\int \frac{dx}{\sqrt{{x}^{2}-25}}$

$=\int \frac{dx}{\sqrt{{x}^{2}-{5}^{2}}}$

Using above mentioned formula, we get,

$\int \frac{dx}{\sqrt{{x}^{2}-{5}^{2}}}=\mathrm{ln}|x+\sqrt{{x}^{2}-25}|+C$ where C is the constant of integration.

Hence,$\int \frac{dx}{\sqrt{{x}^{2}-25}}=\mathrm{ln}|x+\sqrt{{x}^{2}-25}|+C$

Evaluate:

Step 2:Formula used

Step 3:Calculation

Consider the given integral

Using above mentioned formula, we get,

Hence,