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Home  >>  CBSE XII  >>  Math  >>  Integrals
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Integrate the functions\[\frac{1}{\sqrt{(x-1)(x-2)}}\]

$\begin{array}{1 1}\log\mid(x-\frac{3}{2})+\sqrt{x^2-3x+2}\mid+c \\ \log\mid(x+\frac{3}{2})+\sqrt{x^2-3x+2}\mid+c \\ \log\mid(x-\frac{3}{2})-\sqrt{x^2-3x+2}\mid+c \\ \log\mid(x+\frac{3}{2})+\sqrt{x^2+3x+2}\mid+c \end{array} $

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  • $\int\frac{dx}{\sqrt{x^2-a^2}}=log\mid x+\sqrt{x^2-a^2}\mid+c.$
Given:$I=\frac{dx}{(x-1)(x-2)}=\frac{dx}{x^2-3x+2}.$
 
$x^2-3x+2=(x-\frac{3}{2})^2-\frac{1}{4}.$
 
Therfore $I=\int\frac{dx}{(x-\frac{3}{2})^2-\big(\frac{1}{2}\big)^2}$
 
On integrating we get,
 
$\;\;\;=log\mid(x-\frac{3}{2})+\sqrt{x^2-3x+2}\mid+c.$

 

answered Feb 4, 2013 by sreemathi.v
 
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