Does following integral have a solution? $$ \int \exp(-ax^{3/2}+bx) dx $$
Where a and b are constants.
It seems to be straightforward problem but I couldn't find the solution using wolframalpha.
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Well, for $a=b=0$ we have the integral equals $x+c$. – YoTengoUnLCD Nov 15 '15 at 21:20
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2One parameter between $a$ and $b$ is completely useless. Anyway, you may just expand $e^{bx}$ as a Taylor series and perform a termwise integration against $e^{-a x^{3/2}}$. You will get a series that depends on values of the $\Gamma$ function. – Jack D'Aurizio Nov 15 '15 at 21:25
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Why $\Gamma$ function? – Roy Nov 15 '15 at 21:33
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Check this. The third answer has something similar as why you can use a $\Gamma$ function. – Paichu Nov 15 '15 at 22:11