Question

How do I integrate

Answer 1

I know it is by parts, but I can't get the right answer

Answer 2

$$\int xe^{x^2}\,\mathrm{d}x$$We can let \(u=x^2\) and thus \(\mathrm{d}u=2x\,\mathrm{d}x\), which we rearrange to read \(\dfrac12\mathrm{d}u=x\,\mathrm{d}x\). We may now replace:$$\int\color{red}xe^{\color{blue}{x^2}}\color{red}{\,\mathrm{d}x}=\color{red}{\frac12}\int e^{\color{blue}u}\,\color{red}{\mathrm{d}u}$$Can you tackle this?

Answer 3

I understand that you have u in the power of e, but where did the x infront of the e go?

Answer 4

nvm stupid question

Answer 5

let me try to integrate this

Answer 6

http://en.wikipedia.org/wiki/Gaussian_integral

You would not want to integrate by parts because \(\int e^{x^2}\,\mathrm{d}x\) has no elementary result (see: imaginary error function http://en.wikipedia.org/wiki/Error_function).

Answer 7

is this right?