Mathematics

$$\int {\frac{1}{{\left( {x - 1} \right)\left( {x - 2} \right)}}dx} $$


SOLUTION
$$\int \frac{1}{(x-1)(x-2)}dx=\int \frac{(x-1)-(x-2)}{(x-1)(x-2)}dx$$
                          $$=\int\frac{1}{x-2}dx-\int\frac{1}{x-1}dx$$
                           $$=ln\left|x-2\right| -ln\left|x-1\right|+c$$
                           $$=ln\left|\frac{x-2}{x-1}\right|+c$$
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Subjective Medium Published on 17th 09, 2020
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