=

Let’s Say I = I₁ + I₂

And, I_{1 =}

Using Integration By parts

f’ = e^–x, g = x

f = –e^–x, g’ = 1

I₁=

For I₂ =

Using Integration By parts

f’ = e^x, g = x

f = e^x, g’ = 1

I₂=

Now, I = I_{1 +} I₂

==0

Hence, 0