How to show that the integral of sin 1/x is insoluble?

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Homework Statement



Our tutor has given us an equation to think about:

Homework Equations



integral of sin 1/x

I'm pretty sure it's insoluble but how would I go about showing it is?

The Attempt at a Solution



No idea where to start any advice, tried by parts but it ends up in a mess? Not really a proof just because I can't solve it...
 
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I'm not sure what your teacher expects from you. Your suspicion that there is no simple antiderivative expressible with the "usual" functions is correct. Also there is no way you will be able to prove that statement. I would bet that your tutor can't either.
 
Just to be clear is the problem

∫((sin 1)/x) dx

or

∫sin (1/x) dx?

Because one of these is much easier :)
 

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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