Question

what is the anti-derivative of xe^-x^2

Answer 1

(-1/2)e^-x^2

Answer 2

\[\int\limits_{}^{}xe^{-x^2} dx\]

let \[u=-x^2 => du=-2x dx\]

\[\int\limits_{}^{}xe^{-x^2} dx=\frac{-1}{2}\int\limits_{}^{}e^u du\]

Answer 3

hmmm i smell a u-sub
try
\[u=-x^2\]
\[du=-2xdx\] and go from there

Answer 4

d/dx(e^(-x^2) x)
= e^(-x^2) (d/dx(x))+x (d/dx(e^(-x^2)))
= x (e^(-x^2) (d/dx(-x^2)))+e^(-x^2) (d/dx(x))
= e^(-x^2) x (d/dx(-x^2))+1 e^(-x^2)
= e^(-x^2) x (-(d/dx(x^2)))+e^(-x^2)
= e^(-x^2)-e^(-x^2) x (2 x)