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\int\frac{3}{x^2-4x+13}dx

Integral of 3/(-4x+13+x^2)

Answer

$\frac{1}{3}\ln\left|\frac{1}{9}\left(4-4x+x^2\right)+1\right|+C_0$

Step-by-step explanation

Problem

$\int\frac{3}{x^2-4x+13}dx$
1

Add and subtract $\displaystyle\left(\frac{b}{2a}\right)^2$

$\int\frac{3}{-4+4+13-4x+x^2}dx$

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Answer

$\frac{1}{3}\ln\left|\frac{1}{9}\left(4-4x+x^2\right)+1\right|+C_0$