Determine `int e^(3x)/(e^(3x) + 1)^5 dx`

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The integral `int e^(3x)/(e^(3x) + 1)^5 dx` has to be determined.

`int e^(3x)/(e^(3x) + 1)^5 dx`

let `e^(3x) + 1 = y`

`(1/3)*dy = e^(3x) dx`

=> `(1/3)*int 1/y^5 dy`

=> `(1/3)*y^-4/(-4) + C`

=> `-1/(12*y^4) + C`

=> `-1/(12*(e^(3x) + 1)^4) + C`

The integral `int e^(3x)/(e^(3x) + 1)^5 dx = -1/(12*(e^(3x) + 1)^4) + C`

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