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About LinkBacksCan anyone give me any suggestion of how to solve this integral? Or better - has anyone seen any solution to this kind of integral?
I would be grateful for any help!
Originally Posted by Per
Can anyone give me any suggestion of how to solve this integral? Or better - has anyone seen any solution to this kind of integral?
I would be grateful for any help!
Assuming:
Beginning with the first one:![\int^1_0\frac{1}{c+x_1+\ldots +x_n}\,dx_n=[\ln(c+x_1+\ldots +x_n)]^1_0=](http://latex.codecogs.com/png.latex?\int^1_0\frac{1}{c+x_1+\ldots +x_n}\,dx_n=[\ln(c+x_1+\ldots +x_n)]^1_0=)
... I purposedly
didn't write this as the logarithm of a quotient since for the next step is easier to integrate this way.
Next step:-\ln(c+x_1+\ldots +x_{n-1})\right)\,dx_{n-1}=)
![\left[(c+x_1+\ldots +x_{n-1}+1)(\ln(c+x_1+\ldots +x_{n-1}+1)-1)\right]^1_0](http://latex.codecogs.com/png.latex?\left[(c+x_1+\ldots +x_{n-1}+1)(\ln(c+x_1+\ldots +x_{n-1}+1)-1)\right]^1_0)
...etc.
The above doesn't look too hard but it looks pretty messy and ugly...I don't know if there's a nice expression for it all.
Tonio
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