Mathematics

Evaluate:

$$\displaystyle\int _{1}^{2} \left(\dfrac{x-1}{x^{2}}\right)e^{x}dx$$


SOLUTION
$$ \displaystyle \int_{1}^{2} (\frac{x-1}{x^{2}})e^{x}dx $$
$$ \displaystyle \int_{1}^{2} \frac{e^{(x-1)}}{x^{2}}dx $$
$$ \displaystyle \frac{-e^{x}(x-1)}{x}|_{1}^{2}-\int_{1}^{2}-e^{x}dx $$  here $$  \Rightarrow u = e^{x}(x-1);v^{1} = \frac{1}{x^{2}} $$
$$ \displaystyle \frac{-e^{x}(x-1)}{x}+e^{x}|_{1}^{2} $$
$$\displaystyle  \frac{-e^{2}(2-1)}{2}+e^{2}-\frac{e^{1}(1-1)}{1}+e^{1} $$
$$\displaystyle [\frac{-e^{2}}{2}+e^{2}-e] $$
Solution of Given Definite Integral 
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Subjective Medium Published on 17th 09, 2020
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