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Step-by-step Solution

Integral of $\frac{1}{\left(x^2-16^2\right)^{\left(\frac{1}{2}\right)}}$ with respect to x

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Answer

$\ln\left|\frac{x+\sqrt{x^2-36}}{6}\right|+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{dx}{\sqrt[2]{x^2-6^2}}$
1

Calculate the power

$\int\frac{1}{\sqrt{x^2-1\cdot 36}}dx$
2

Apply the formula: $-x$, where $x=36$

$\int\frac{1}{\sqrt{x^2-36}}dx$

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Answer

$\ln\left|\frac{x+\sqrt{x^2-36}}{6}\right|+C_0$
$\int\frac{dx}{\sqrt[2]{x^2-6^2}}$

Main topic:

Integrals of Rational Functions

Used formulas:

6. See formulas

Time to solve it:

~ 1.01 seconds