Integration of complex funcion

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fenixtx423

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Is there any way to calculate the indefinite integral cleanly of this function? I am integrating as a function of x, and all other values are constants.

((x-c+d)/(2*d))^0.5*((1+x/a)^-b-((x*b)/a)*(1+x/a)^(-b-1))

MSP3511d935d18833c8ci700003i50i1g0e5g671fe


I have tried the online integration calculators, and they either do not work or give results with hypergeometric functions.

This is for a research project I am working on involving random fields and spatial correlation.
 
Last edited:
Not sure if this is useful at all, but the function on the right can be written as a derivative as shown below:

MSP16101ede46adde8e5h3d00002aha4g223264i67g
 
fenixtx423 said:
Is there any way to calculate the indefinite integral cleanly of this function? I am integrating as a function of x, and all other values are constants.

((x-c+d)/(2*d))^0.5*((1+x/a)^-b-((x*b)/a)*(1+x/a)^(-b-1))

MSP3511d935d18833c8ci700003i50i1g0e5g671fe


I have tried the online integration calculators, and they either do not work or give results with hypergeometric functions.

This is for a research project I am working on involving random fields and spatial correlation.
Click to expand...
Not sure if this is useful at all, but the function on the right can be written as a derivative as shown below:

MSP16101ede46adde8e5h3d00002aha4g223264i67g
Click to expand...

Did you try integration by parts?
 
fenixtx423 said:
Is there any way to calculate the indefinite integral cleanly of this function? I am integrating as a function of x, and all other values are constants.

((x-c+d)/(2*d))^0.5*((1+x/a)^-b-((x*b)/a)*(1+x/a)^(-b-1))

MSP3511d935d18833c8ci700003i50i1g0e5g671fe


I have tried the online integration calculators, and they either do not work or give results with hypergeometric functions.

This is for a research project I am working on involving random fields and spatial correlation.
Click to expand...
You can simplify it to: [(x+r)^.5]/(s+x)-(t+x)*(u+x)^(-b-1)
 
fenixtx423 said:
Is there any way to calculate the indefinite integral cleanly of this function? I am integrating as a function of x, and all other values are constants.

((x-c+d)/(2*d))^0.5*((1+x/a)^-b-((x*b)/a)*(1+x/a)^(-b-1))

MSP3511d935d18833c8ci700003i50i1g0e5g671fe


I have tried the online integration calculators, and they either do not work or give results with hypergeometric functions.

This is for a research project I am working on involving random fields and spatial correlation.
Click to expand...

Why are you not accepting the hypergeometric function? As long as you leave the constants in a general form you will always get the general hypergeometric function. Note that in some special cases the hypergeometric function can reduce to a polynomial, see
http://en.wikipedia.org/wiki/Hypergeometric_function
for example
 
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