x\,dx/(x-1)(x-2) equals - NCERT Class XII Mathematics Chapter

NCERT Class XII Mathematics Chapter - - Solutions

Choose the correct answer in each of the Exercises 132 and 133.

Question : 132 of 271

Marks: +1, -0

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

equals

Solution:

Let

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

=\int \left[ \frac{-1}{x-1}+\frac{2}{x-2} \right]\,dx

=-\log(x-1)+2\log(x-2)+C

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

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