"Use a table of integrals to evaluate the..." was answered by our experts

cleritere39

Answered question

2021-11-07

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

\int \frac{d x}{\sqrt{x^{2} - 25}}

Answer & Explanation

Louise Eldridge

Beginner2021-11-08Added 17 answers

Step 1:To determine
Evaluate:

\int \frac{d x}{\sqrt{x^{2} - 25}}

Step 2:Formula used

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

Step 3:Calculation
Consider the given integral

\int \frac{d x}{\sqrt{x^{2} - 25}}

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

Using above mentioned formula, we get,

\int \frac{d x}{\sqrt{x^{2} - 5^{2}}} = \ln | x + \sqrt{x^{2} - 25} | + C

where C is the constant of integration.
Hence,

\int \frac{d x}{\sqrt{x^{2} - 25}} = \ln | x + \sqrt{x^{2} - 25} | + C

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