# How to integrate #1/sqrt(x^2 - 4x + 3) dx #?

Complete the square at the denominator:

and subtitute:

Note also that:

and the integrand function is defined for

Then:

Use now the trigonometric identity:

so:

Then:

and to undo the substitution we note that:

so:

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To integrate ( \frac{1}{\sqrt{x^2 - 4x + 3}} ) with respect to ( x ), you can use a trigonometric substitution method. Let ( x - 2 = \sqrt{3} \sec(\theta) ). Then solve for ( x ) in terms of ( \theta ). After substitution, simplify the integrand, perform the integration with respect to ( \theta ), and then resubstitute back to ( x ) after integration.

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