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
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