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Question
`int(x + 1/x)^3 dx` = ______.
Options
`1/4(x + 1/x)^4 + c`
`x^4/4 + (3x^2)/2 + 3log x - 1/(2x^2) + c`
`x^4/4 + (3x^2)/2 + 3log x + 1/x^2 + c`
`(x - x^(-1))^3 + c`
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Solution
`int(x + 1/x)^3 dx` = `bb(underline(x^4/4 + (3x^2)/2 + 3log x - 1/(2x^2) + c))`.
Explanation:
`(x + 1/x)^3 = x^3 + 3x + 3/x + 1/x^3`
∴ `int(x + 1/x)^3dx = int(x^3 + 3x + 3/x + 1/x^3)dx`
= `x^4/4 + (3x^2)/2 + 3logx - 1/(2x^2) + c`
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