Mathematics

Solve $$\int \dfrac { d t } { t ( t + 1 ) }$$


SOLUTION
$$\displaystyle\int{\dfrac{dt}{t\left(t+1\right)}}$$

$$=\displaystyle\int{\dfrac{\left(t+1-t\right)dt}{t\left(t+1\right)}}$$

$$=\displaystyle\int{\dfrac{\left(t+1\right)dt}{t\left(t+1\right)}}-\displaystyle\int{\dfrac{tdt}{t\left(t+1\right)}}$$

$$=\displaystyle\int{\dfrac{dt}{t}}-\displaystyle\int{\dfrac{dt}{\left(t+1\right)}}$$

$$=\log{\left|t\right|}-\log{\left|t+1\right|}+c$$

$$=\log{\left|\dfrac{t}{t+1}\right|}+c$$
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Subjective Medium Published on 17th 09, 2020
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