cleritere39

2021-11-07

Use a table of integrals to evaluate the following indefinite integral.
$\int \frac{dx}{\sqrt{{x}^{2}-25}}$

Louise Eldridge

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

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