The value of ed∫e5x(1x-15x2) dx is ______. - Mathematics

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The value of `int "e"^(5x) (1/x - 1/(5x^2))  "d"x` is ______.

Options

  • `"e"^(5x)/5 + "c"`

  • `"e"^(5x)/(5x) + "c"`

  • `"e"^(5x)/x + "c"`

  • `5"e"^(5x) + "c"`

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Solution

The value of `int "e"^(5x) (1/x - 1/(5x^2))  "d"x` is `"e"^(5x)/(5x) + "c"`.

Explanation:

`int "e"^(5x) (1/x - 1/(5x^2))  "d"x = "e"^(5x)/(5x) + "c"`  .......`[because "e"^(mx) ["f"(x) + ("f'"(x))/"m"] "d"x = ("e"^(mx)"f"(x))/"m" + "c"]`

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