∫e3xe3x+1 dx - Mathematics and Statistics

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Sum

`int ("e"^(3x))/("e"^(3x) + 1)  "d"x`

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Solution

Let I = `int ("e"^(3x))/("e"^(3x) + 1)  "d"x`

Put e3x + 1 = t

Differentiating w.r.t. x, we get

3e3xdx = dt

∴ e3xdx = `"dt"/3`

∴ I = `int 1/"t"* "dt"/3 = 1/3  log  |"t"| + "c"`

∴ I  `1/3 log|"e"^(3x) + 1| + "c"`

  Is there an error in this question or solution?
Chapter 2.3: Indefinite Integration - Very Short Answers

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