Mathematics

# $I=\displaystyle \int \dfrac{(x+a)^3}{x^3}dx$ is equal to:

$x+ 3a \log x -\dfrac{3a^2}{x} - \dfrac{a^3}{2x^2}+c$

##### SOLUTION
$I=\displaystyle \int \dfrac{(x+a)^3}{x^3}dx$

$=\displaystyle \int \dfrac {x^{3}+a^{3}+3ax^{2}+3a^{2}x}{x^{3}}dx$

$=\displaystyle \int \left (1+\dfrac {a^{3}}{x^{3}}+\dfrac {3a}{x}+\dfrac {3a^{2}}{x^{2}}\right) dx$

$=x-\dfrac {a^{3}}{2x^{2}}+3a\log x - \dfrac {3a^{2}}{x}+c$

$=x+3a\log x - \dfrac {3a^{2}}{x}-\dfrac {a^{3}}{2x^{2}}+c$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

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