Question

What is `int (8x)/e^(x^2) \ dx`?

Answer 1

I got: `-4e^(-x^2)+c`

Explanation:

Have a look:

Answer 2

`int (8x)/e^(x^2) \ dx = -4 e^(-x^2) + c`

Explanation:

We seek:

`I = int (8x)/e^(x^2) \ dx`

Which we can write as:

`I = -4 \ int (-2x)e^(-x^2) \ dx`

With practice we can integrate this directly, but for the benefit of those unable to do this, let us perform substitution:

Let `u=e^(-x^2) => (du)/dx = -2xe^(-x^2)`

So if we now substitute this into the integral, we get:

`I = -4 \ int \ du`

Which is now a standard integral, so we have:

`I = -4 u + c`

And reversing the substitution:

`I = -4 e^(-x^2) + c`