# How to evaluate this integral with exponent of an exponent?

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?

• You might consider writing $x^{x^2} = \exp(\log(x^{x^2}))$ and simplifying things a bit. Then try a substitution. – Xander Henderson Nov 18 '18 at 16:17
• maybe a parameterization so that you could differentiate under the integral sign? – clathratus Nov 18 '18 at 21:38
• @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... – blizz Nov 20 '18 at 1:11
• $\exp(t) = \mathrm{e}^t$. – Xander Henderson Nov 20 '18 at 1:42