Choose the correct alternative: ∫(x+1x)3dx = ______. - Mathematics and Statistics

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Choose the correct alternative:

`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`

  Is there an error in this question or solution?
Chapter 1.5: Integration - Q.1

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