How to solve the integral $$\int x\cdot 9\cdot x^{2x^2} dx$$
I tried $u=2x^2$ and $du= 4x\;dx\Longrightarrow$ $$\int x\cdot9\cdot x^{2x^2}\;dx=\frac94\int x^u du$$But it was unable to pass.
2026-04-15 13:15:32.1776258932
How to solve the integral $\int x\cdot 9\cdot x^{2x^2} dx$
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$x^{2x^2}=(x^2)^{x^2}=y^y$ . Also, $y'(x)=(x^2)'=2x$. Then our integral becomes $\displaystyle\frac92\int y^ydy$ , which, despite looking much prettier, is however still not expressible in terms of elementary functions. :-)