Is there a "formal" counterpart (or equivalent) to the process of differentiation by first principle for computing integral?
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I would be quite surprised if the primitive is elementary, since WolframAlpha isn't even trying. – DHMO Apr 16 '17 at 10:10
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Maybe you want to know $\int_0^\infty \sin x/(x^3+\sqrt{x}) dx$? There is better chance for an explicit expression for the definite integral. – Fabian Apr 16 '17 at 10:17
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4By letting $x=t^2$ and applying PFD over complex numbers, you'll get integrals of the form $\int\frac{\sin(t^2)}{t-a}\ dt$. From there, replace sine with its complex exponential definition and use incomplete gamma functions. – Simply Beautiful Art Apr 16 '17 at 10:24
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@simplybeautifulart what is PFD in this context? – unseen_rider Apr 16 '17 at 10:39
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@unseen_rider Partial fraction decomposition. – Simply Beautiful Art Apr 16 '17 at 11:20
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user12345 Do not change your original question here, to one that is very much unrelated to this original. – amWhy May 06 '17 at 14:38