Solving Divergent Integral: -infinity Correct?

n.a.s.h
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Homework Statement


I had to solve the integral...After all my work i got -infinity
3
integral sign 1/ [(t-3)^4/3]
1


Homework Equations





The Attempt at a Solution


-infinity...is this correct? and would this be divergent?
 
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The expression

<br /> \frac{1}{(t - 3)^{4/3}}<br />

is complex for t &lt; 3.
 
Yes, it is divergent.
 
It has a real root for t<3, so that's not a problem. I would check how you got the sign on that -\infty, though.
 

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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