Mathematics

The value of $$\int { { e }^{ 2x } } \left(\dfrac{1}{x} - \dfrac{1}{2x^2}\right)$$ dx is 


SOLUTION
Let $$2x=t$$
$$\Rightarrow 2dx=dt$$
$$\Rightarrow I=\displaystyle\int e^t\left(\dfrac{2}{t}-\dfrac{4}{2t^2}\right)\dfrac{dt}{2}$$
$$=\displaystyle\int e^t\left(\dfrac{1}{t}-\dfrac{1}{t^2}\right)dt$$
$$=$$ of form $$\displaystyle\int e^x(f(x)+f'(x))dx$$
$$=e^xf(x)+c$$
$$\Rightarrow I=e^t\left(\dfrac{1}{t}\right)+c$$
$$\Rightarrow I=\dfrac{e^{2x}}{2x}+c$$

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Subjective Medium Published on 17th 09, 2020
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