{1}{{(x-1)(x-2)}} - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.4
Integrate the functions in Exercises 86 to 108.

Question : 98 of 271

Marks: +1, -0

\frac{1}{\sqrt{(x-1)(x-2)}}

Solution:

Let

I=\int \frac{1}{\sqrt{(x-1)(x-2)}}\,dx

=\int \frac{dx}{\sqrt{x^2-3x+2}}

=\int \frac{dx}{\sqrt{x^2 - 2 \cdot \frac{3}{2}x + \frac{9}{4} + 2 - \frac{9}{4}}}

=\int \frac{dx}{\sqrt{\left(x-\frac{3}{2}\right)^2 - \left(\frac{1}{2}\right)^2}}

=\log\left| \left(x-\frac{3}{2}\right) + \sqrt{\left(x-\frac{3}{2}\right)^2 - \left(\frac{1}{2}\right)^2} \right| + C

=\log\left| \left(x-\frac{3}{2}\right) + \sqrt{(x-1)(x-2)} \right| + C

Go to Question: