I got this on a Calc 2 test as an MCQ. I have no idea how to think about this
2026-05-05 02:58:39.1777949919
Why is this integral not integrable?
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Just written for your curiosity.
If the expression was $$I=k \int_a^be^x (x-1) \sqrt{x} \log \left(x^2\right)\,dx$$ we could have an analytical solution in terms of special functions since $$\int e^x (x-1) \sqrt{x} \log \left(x^2\right)\,dx=-\frac{8}{25} x^{5/2} \, _2F_2\left(\frac{5}{2},\frac{5}{2};\frac{7}{2},\frac{7}{2};x\right)+\frac{8}{9} x^{3/2} \, _2F_2\left(\frac{3}{2},\frac{3}{2};\frac{5}{2},\frac{5}{2};x\right)+\frac{1}{4} \left(5 \sqrt{\pi } \text{erfi}\left(\sqrt{x}\right)+2 e^x \sqrt{x} (2 x-5)\right) \log \left(x^2\right)$$ where appear hypergeometric functions.
Nice, isn't it ?