Show that $$\int_0^\infty dx\exp(ikx^3) , k>0$$ may be written as integral from 0 to ##\infty## along the line ##arg(z) = \frac{\pi}{6}##.(adsbygoogle = window.adsbygoogle || []).push({});

I'd appreciate it if you can help me how to approach this problem. My initial impression was to expand the integrand out

$$\sum^{\infty}_{n=0}\frac{(ikx^3)^n}{n!}$$

but did not how to obtain the ##arg(z)## condition. I plugged the integral in wolframalpha and gave me an expression with a Gamma function, which the lecture has covered but I'm not sure how to apply here.

Thanks

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# I Integral e^(ikx^3)

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