Whats the integral of xe^(-x)

Ciara Rose 2022-07-26 Answered
Whats the integral of x e x
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Answers (2)

losnonamern
Answered 2022-07-27 Author has 12 answers
In order to use substitution, one part of the integrand must be the derivative of the other part...that is not the case here. to integrate the above equation requires integration by parts.
x e x d x
u d v = u v v d u
let:
u=x and d v = e x d x
then
du=dx and v = e x
plugging in.
x e x d x = x e x d x = x e x e x + C = e x ( x + 1 ) + C
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Makena Preston
Answered 2022-07-28 Author has 3 answers
integration by parts:
let u= x d v = e x d x
du= dx v = e x
so u v v d u = x ( e x ) ( e x ) d x
= x e x + e x d x [use u-sub to solve integral: let u = x d u = d x]
= x e x e x + C
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