Find the integral int(1/(x^2-12x+180))dx

 Exercise

$\int\frac{1}{x^2-12x+180}dx$

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Solve the integral by applying the formula $\displaystyle\int\frac{x'}{x^2+a^2}dx=\frac{1}{a}\arctan\left(\frac{x}{a}\right)$

$\frac{1}{\sqrt{180-12x}}\arctan\left(\frac{x}{\sqrt{180-12x}}\right)$

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Multiply the fraction by the term

$\frac{\arctan\left(\frac{x}{\sqrt{180-12x}}\right)}{\sqrt{180-12x}}$

 

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$\frac{\arctan\left(\frac{x}{\sqrt{180-12x}}\right)}{\sqrt{180-12x}}+C_0$

$\frac{\arctan\left(\frac{x}{\sqrt{180-12x}}\right)}{\sqrt{180-12x}}+C_0$

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