Evaluate the integral. $$ \int \frac{d x}{x^{2} \sqrt{x^{2}-25}}, x5 $$

Question

Evaluate the integral. $$ \int \frac{d x}{x^{2} \sqrt{x^{2}-25}}, x>5 $$

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Calculate the integral $$ \int \frac{1}{x^{2} \sqrt{x^{2}-25}} dx $$.
Evaluate the integral by following steps:
- step0: Evaluate using formulas and rules:
  $$\int \frac{1}{x^{2}\sqrt{x^{2}-25}} dx$$
- step1: Evaluate the integral:
  $$\frac{\sqrt{x^{2}-5^{2}}}{5^{2}x}$$
- step2: Evaluate the power:
  $$\frac{\sqrt{x^{2}-25}}{5^{2}x}$$
- step3: Simplify:
  $$\frac{\sqrt{x^{2}-25}}{25x}$$
- step4: Add the constant of integral C:
  $$\frac{\sqrt{x^{2}-25}}{25x} + C, C \in \mathbb{R}$$
The integral of $$\frac{1}{x^{2} \sqrt{x^{2}-25}}$$ with respect to $$x$$ is $$\frac{\sqrt{x^{2}-25}}{25x} + C$$, where $$C$$ is an arbitrary constant.
The integral evaluates to $$ \frac{\sqrt{x^{2}-25}}{25x} + C $$.

Evaluate the integral.

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