Homework Help

How do integrate function  `int (3x^2)/e^(x^3) dx`  ?

user profile pic

techmicha | Student, Undergraduate | eNoter

Posted August 21, 2012 at 12:05 PM via web

dislike 2 like

How do integrate function  `int (3x^2)/e^(x^3) dx`  ?

Tagged with integrate function, math

1 Answer | Add Yours

user profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted August 21, 2012 at 12:16 PM (Answer #1)

dislike 1 like

You need to evaluate indefinite integral `int (3x^2)/(e^(x^3)) dx`  using substitution such that:

`x^3 = y =gt 3x^2 dx = dy`

You need to change the variable such that:

`int (dy)/(e^(y)) = int e^(-y) dy `

`int e^(-y) dy = -e^(-y)+ c`

You need to substitute `x^3`  for `y`  such that:

`int (3x^2)/(e^(x^3)) dx = -e^(-x^3) + c`

Hence, evaluating the indefinite integral yields `int (3x^2)/(e^(x^3)) dx = -e^(-x^3) + c`

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes