Homework Help

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

user profile pic

good2beme | Student, Undergraduate | (Level 1) Honors

Posted July 16, 2012 at 1:21 AM via web

dislike 2 like

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

1 Answer | Add Yours

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 16, 2012 at 2:03 AM (Answer #1)

dislike 1 like

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`

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes