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What technique should i use to integrate $\int(4-x)^{1/4}e^{\frac{1}{2}x}dx?$

Ive tried to use algebraic manipulation and integration by parts but it just became complicated.

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    @Hurkyl Yes i am actually working on a definite integral from$0$to 4.2012-10-25

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The change of variable $x=4-2z$ yields $\int_0^4(4-x)^{1/4}\mathrm e^{x/2}\mathrm dx=2^{1/4}\mathrm e^2\int_0^2z^{1/4}\mathrm e^{-z}\mathrm dz=2^{1/4}\mathrm e^2\cdot\gamma(5/4,2), $ where $\gamma$ is the lower incomplete gamma function.

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    Not sure what you are asking but $(d/dx)\gamma(a,x)=x^{a-1}e^{-x}$.2012-10-29