Question

integrate (x+1/x)^3
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Answer 1

$\huge \bold {\red {\underline{\mathfrak{ANSWER}}}} \red{ :}$

$\huge \int{ ({ \frac{x + 1}{x}) }^{3} } \\ \longrightarrow \: \int \frac{ {x}^{3} + 3 {x}^{2} + 3x + 1 }{ {x}^{3} } dx \\ \longrightarrow \: \int \: (1 + \frac{3}{x} + \frac{3}{ {x}^{2} } + \frac{1}{ {x}^{3} }) dx \\ \longrightarrow \int {1} \: dx + \int \frac{3}{x} dx + \int \frac{3}{ {x}^{2} } dx + \int \frac{1}{ {x}^{3} } dx \\ \longrightarrow x + x ln( |x| ) - \frac{x}{3} - \frac{1}{2 {x}^{2} } + c$

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