I have the following integral which I need to evaluate but don't even know where to begin other than knowing I need to use u-substitution: $$\int_1^\sqrt{3}2x^{x^{2}}$$

So far I know that $u=x^{2}$ and $du=2x$ but how do I evaluate this?

  • 1
    $\begingroup$ You might consider writing $x^{x^2} = \exp(\log(x^{x^2}))$ and simplifying things a bit. Then try a substitution. $\endgroup$ – Xander Henderson Nov 18 '18 at 16:17
  • $\begingroup$ maybe a parameterization so that you could differentiate under the integral sign? $\endgroup$ – clathratus Nov 18 '18 at 21:38
  • $\begingroup$ @XanderHenderson what does it mean to write exp(log(x^x^2))? I might be a little slow now but not sure what that exp does... $\endgroup$ – blizz Nov 20 '18 at 1:11
  • $\begingroup$ $\exp(t) = \mathrm{e}^t$. $\endgroup$ – Xander Henderson Nov 20 '18 at 1:42

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