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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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