Mathematics

Solve:
$$\int {{e^x}} \left( {\frac{{x - 1}}{{{x^2}}}} \right)dx$$


SOLUTION

$$\int e^x(\dfrac{x-1}{x^2})dx$$

$$=\int e^x (\dfrac{1}{x}-\dfrac{1}{x^2})dx$$

$$=\int e^x(\dfrac{1}{x})dx$$$$-$$$$\int e^x\dfrac{1}{x^2}dx$$

$$=\dfrac{1}{x}\int e^x dx$$$$-$$$$\int \dfrac{d}{dx} \dfrac{1}{x}$$$$\int e^x dx)dx$$$$-$$$$\int e^x \dfrac{1}{x^2}dx$$

$$=\dfrac{1}{x} e^x$$$$-$$$$\int \dfrac{-1}{x^2} e ^xdx$$$$-$$$$\int e^x \dfrac{1}{x^2} dx$$

$$=\dfrac{e^x}{x}$$$$+$$$$c$$

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Subjective Medium Published on 17th 09, 2020
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