Could you please help me in solving the following integration. Thank you in advance.
Integrate[((Sqrt[g*(x + h)/y])^V) * Exp[-u * Sqrt[g*(x + h)/y]/n] * Exp[-L*x], {x, 0, Infinity}]
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Sign up to join this communityCould you please help me in solving the following integration. Thank you in advance.
Integrate[((Sqrt[g*(x + h)/y])^V) * Exp[-u * Sqrt[g*(x + h)/y]/n] * Exp[-L*x], {x, 0, Infinity}]
I assumed the parameters are positive real numbers. One could simplify things a little by replacing g/y
by a
and u/n
by b
— the more parameters, the harder you make it for Mathematica.
Integrate
evaluates in the special case h = 0
, but not for other values of h
tested.
Clear[g, L, x, h, y, V, n, u];
Block[{h = 0},
Integrate[((Sqrt[g*(x + h)/y])^V)*Exp[-u*Sqrt[g*(x + h)/y]/n]*
Exp[-L*x], {x, 0, Infinity},
Assumptions -> V > 0 && g > 0 && u > 0 && n > 0 && L > 0 && y > 0]
]
(*
(2^(-1 - V) ((L y)/g)^(-V/2)
Gamma[2 + V] HypergeometricU[1 + V/2, 1/2, (g u^2)/(4 L n^2 y)])/L
*)
It evaluates if only V
is given numeric values (in all tests):
Block[{g, h, V = 3, L, n, u, y},
Integrate[((Sqrt[g*(x + h)/y])^V)*Exp[-u*Sqrt[g*(x + h)/y]/n]*
Exp[-L*x], {x, 0, Infinity},
Assumptions ->
V > 0 && g > 0 && u > 0 && n > 0 && L > 0 && y > 0 && h > 0]
]
The remaining cases probably cannot be done.