Integrating e^(8x^2) - Solutions & Steps

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Homework Statement



integerate e^(8x^2)

Homework Equations





The Attempt at a Solution



its seems it is not having closed integeral form.
 
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They're asking you to take an indefinite integral of that? It doesn't have an elementary antiderivative, but the erf(x) is used to take definite integrals, so if they haven't taught you about that, I'm guessing you have the problem wrong.
 
no erff function can be integerated i guess
 
some wolfram but i don't know how i could use dat formulae here!
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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