Whats the integral of x e − x

Question

Whats the integral of   x      e          −      x

losnonamern · Accepted Answer

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.

\int x e^{- x} d x

\int u d v = u v - \int v d u

let:
u=x and

d v = e^{- x} d x

then
du=dx and

v = - e^{- x}

plugging in.

\int x e^{- x} d x = - x e^{- x} d x = - x e^{- x} - e^{- x} + C = - e^{- x} (x + 1) + C

Makena Preston · Accepted Answer

integration by parts:let u= x            d  v  =      e          −      x        d  xdu= 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

Whats the integral of xe^(-x)

Answered question

Answer & Explanation

New Questions in Integral Calculus