Question

integral of e^(-x^2)x dx

Answer 1

\[\large \int e^{-x^2}xdx\]

If we let \(\large u = -x^2\) that means \(\large du = -2xdx\)

Now notie we need to get \(\large xdx\) but now we have \(\large -2xdx\) so lets divide everything by -2

\[\large -\frac{1}{2} \int e^{u}du\]

And we know the integral of e^x = e^x so

\[\large -\frac{1}{2}e^u +c\]

Now lets just replace back in 'u' in terms of 'x'

\[\large -\frac{1}{2}e^{-x^2} + c\]