Mathematics

Evaluate :$\displaystyle \int { { \left( x+\dfrac { 1 }{ x } \right) }^{ 3 } } dx,x>0$

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

$\displaystyle \Rightarrow \int \left(x^{3}+\frac{1}{x^{3}}+3x^{2}\frac{1}{x}+3x.\frac{1}{x^{2}}\right)dx$

$\displaystyle \Rightarrow \int \left(x^{3}+\frac{1}{x^{3}}+3x+\frac{3}{x}\right)dx$

$\displaystyle \Rightarrow \frac{x^{4}}{4}+\frac{x^{-3+1}}{-3+1}+\frac{3x^{2}}{2}+3 \log x$

$\displaystyle \Rightarrow \frac{x^{4}}{4}-\frac{1}{2x^{2}}+\frac{3x^{2}}{2}+3\log x+c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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