MHB Integral with sinx in the denominator

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SUMMARY

The integral $$\int \frac{x}{\sin x} \, dx$$ does not have an elementary anti-derivative. The user attempted u-substitution with $$u = \sin x$$, which led to an incorrect formulation of the integral. Integration by parts was suggested as a potential method, but the discussion concluded that simplifying the expression further is necessary to approach the problem effectively.

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I have this integral

$$\int_{}^{} \frac{x}{sinx} dx$$

How can I approach solving this? I tried u-substitution with $u = sinx$. And I get

$$\int_{}^{} \frac{x}{cosx u} du$$, so I don't think that is an option. I'm also unsure of how I would apply integration by parts. Or can I simplify the expression in some way to make this easier?
 
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That particular integrand does not have an anti-derivative expressible in elementary terms. :)
 
Regardless of the function not having an elementary anti-derivative, your substitution is wrong.
 

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