I=∫dxx^2 6x+13 I=∫dx(x 3)^2+13 9 I=∫dx(x 3)^2+4 I=∫dx(x 3)^2+2^2 I=12 tan^ 1x 32+C ...

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Integration of Irrational Algebraic Fractions - 1

Find ∫dx/x2...

Question

Find $\int \frac{d x}{x^{2} - 6 x + 13}$

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Solution

$I = \int \frac{d x}{x^{2} - 6 x + 13}$

$I = \int \frac{d x}{(x - 3)^{2} + 13 - 9}$

$I = \int \frac{d x}{(x - 3)^{2} + 4}$

$I = \int \frac{d x}{(x - 3)^{2} + 2^{2}}$

$I = \frac{1}{2} t a n^{- 1} \frac{x - 3}{2} + C$

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