Problem using integral in a nonlinear system

Hello, I'm trying to solve a 4x4 nonlinear system of equations (using fsolve and lsqnonlin). Two of these equations have integrals, so at first use "int" in them, however, they do not have explicit solutions. So after try to solve using "integral" instead of "int", but not work either. I think the problem is with the integrals, because attempts to calculate it separately I get no results. The integral is:

integral((18000000*(1740853180245066011576893440000000*lambda10 + 518109338505567084173161632431603712*exp(t/10) - 51810602260580064227258209148465058700*t^2*exp(t/10) - 263671875*7452311944676252099^(1/2)*exp(t/20)*(12952650565145016056814552287116264675*t^2*exp(t/10) - 129527334626391771043290408107900928*exp(t/10) - 435213295061266502894223360000000*lambda10)^(1/2) + 5273437500*7452311944676252099^(1/2)*t*exp(t/20)*(12952650565145016056814552287116264675*t^2*exp(t/10) - 129527334626391771043290408107900928*exp(t/10) - 435213295061266502894223360000000*lambda10)^(1/2)))/(435213295061266502894223360000000*lambda10 + 129527334626391771043290408107900928*exp(t/10) - 12952650565145016056814552287116264675*t^2*exp(t/10)),tau,T1)

where even after giving values to the constants that I want to find (lambda10, tau, T1), gives me the following error: "Error using integralCalc / finalInputChecks (line 515) Output of the function must be the same size as the input. If FUN is an array-valued integrand, Set the 'ArrayValued' option to true.

Error in integralCalc / iterateScalarValued (line 315)                  finalInputChecks (x, fx);

Error in integralCalc / vadapt (line 133)              [q, errbnd] = iterateScalarValued (u, TInterval, pathlen);

Error in integralCalc (line 76)          [q, errbnd] = vadapt (@ AtoBInvTransform, interval);

Error in integral (line 89) IntegralCalc Q = (fun, a, b, opstruct); "

Please help!!

[Jurgen]

I forgot to mention that before having the error I posted in the previous comment, first had an error saying: "Error using ^ Inputs must be a scalar and a square matrix. To compute elementwise POWER, use POWER (^.) Instead. "And" Error using * Inner matrix dimensions must agree. ".

Fix it by changing ^. ^ Y * by. *, But not really understand porqu telling me this because all the unknowns are scalar.

Answer 1

[Matt J]

Do as the error message instructs and call integral() with the 'ArrayValued' option set to true.

[Jurgen]

thanks a lot! Now I'll see if I can solve the system