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I am trying to solve the following integral

$$\int_{0}^{\infty}e^{-(ax+bx^c)}\,dx ; ~~~a,b,c>0.$$

I tried using partial functions but that didn't lead to anything.

Any suggestion?

ALPHA
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    Given that that does not have a closed form for $c=2$ (except using the error function or normal cdf or when $a=0$), what makes you think it might have a solution? – Henry Jan 12 '16 at 16:35

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