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I think this problem requires integration by substitution and integration by parts, but I seem to get stuck each time I try to solve it. And I'm not sure whether '$u$' should be equal to $\sqrt{2}$ or $\sqrt{2}\sqrt{x}$.

Thank you in advance for any help.

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Setting $t=\sqrt{2x}$, we get $x=\frac{t^2}{2}$ and $dx=tdt$ we get the integral $\int te^{t}dt$ in a few minutes.

I will post the solution: setting $u=t$ and $v'=e^{t}$, we obtain $u'=1$ and $v=e^{t}$. Thus we have $\int te^{t}dt=te^{t}-e^{t}+C$.

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  • $\begingroup$ Maybe mention explicitly that you're using integration by parts? The OP sounds inexperienced with these types of problems, and could use as much guidance as possible. $\endgroup$
    – Matt R.
    Oct 21, 2014 at 11:58
  • $\begingroup$ I'm aware, I'm not that incompetent haha $\endgroup$
    – rferguson
    Oct 22, 2014 at 11:09

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