Can You Solve This Integral?

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SUMMARY

The integral \(\int_{-\infty}^{\infty} e^{\lambda x^{2}} dx\) has specific solutions based on the value of \(\lambda\). For \(\lambda > 0\) and \(\lambda = 0\), the integral diverges and does not exist. However, when \(\lambda < 0\), the solution is definitively \(\sqrt{\pi/|\lambda|}\). This conclusion is well-established in mathematical literature.

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Frankww
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I've got a difficult integral, that is, [tex]\int_{-\infty}^{\infty} e^{\lambda x^{2}} dx[/tex]. Could anybody find its solution?
 
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Try http://integrals.wolfram.com/index.jsp"
 
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Since, for [itex]\lambda> 0[/itex], that is not bounded as x goes to infinity, and, if [itex]\lambda= 0[/itex], that is just [itex]\int_{-\infty}^{\infty} dx[/itex], neither of those exists.

If, however, [itex]\lambda[/itex] is negative, It is well known that the integral is
[itex]\sqrt{\pi/|\lambda |}[/itex].
 

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