# Integral problem

Can you you solve this Integral problem

Dear Friends
Can youn help me to integrate the follownig formula
L.H.S = Integrate[1-6*Lambda/x*Coth(x/2*Lambda)+12*(Lambda^2/x^2))*x^3*g(x)dx] / Integrate[x^3*g(x)dx]
Where g(x) = a*exp[-0.5/b^2*ln(x/x0)^2] is the distribution function
where a= 51.5801
b=0.9585
x0=5.4073
I like to solve for Lambda, where the L.H.S is determined experimentally
Thank you very much for your cooperation.

Last edited:

saltydog
Homework Helper
princepolo said:
Dear Friends
Can youn help me to integrate the follownig formula
L.H.S = Integrate[1-6*Lambda/x*Coth(x/2*Lambda)+12*(Lambda^2/x^2))*x^3*g(x)dx] / Integrate[x^3*g(x)dx]
Where g(x) = a*exp[-0.5/b^2*ln(x/x0)^2] is the distribution function
where a= 51.5801
b=0.9585
x0=5.4073
I like to solve for Lambda, where the L.H.S is determined experimentally
Thank you very much for your cooperation.

Hey Prince. That's hard to follow. Welcome to PF. We use LaTex in here and you may wish to learn to use it if you post frequently. Check out the thread in the Physics Forum about using LaTex. This is what I think it is:

$$\frac{\int_u^v \left(1-\frac{6\lambda}{x}Coth(\frac{\lambda x}{2})+12(\frac{\lambda^2}{x^2})x^3 g(x)\right)dx}{\int_u^v x^3 g(x)dx}$$

With u and v as the limits of integration

Maybe that's close. Correct it if necessary. Really, I'd just program it into Mathematica as a function and solve it numerically:

f($\lambda$)=NIntegrate[g(x,$\lambda$),{x,u,v}]

Plot it for starters and see where the LHS meets your value. Then can use NSolve:

NSolve[f($\lambda$)==my value]

(or whatever else it takes in Mathematica to get a numerical answer)