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.
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.
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.