error while using solve function with integral

Please suggest the solution for the encoutering problem below:

syms x V; Pr=solve( int(x.^2.* exp(-x-1./(x+V)),x,1,inf )-0.5 ==0,V);

Answer 1

[Walter Roberson]

That equation has no real-valued solution. Are you expecting a complex-valued solution?

[modem sudhakar]

No walter, I am expecting real value solution. The value of 'C' can be varied in the program below. At what value of 'C', I can obtain real value.

C=0.5; syms x V; Pr=solve( int(x.^2.* exp(-x-1./(x+V)),x,1,inf )-C ==0,V);

How you find that it will result complex-value?. While I am running it is giving the error like below:

syms x V; Pr=solve( int(x.^2.* exp(-x-1./(x+V)),x,1,inf )-0.5 ==0,V);
Warning: Explicit integral could not be found. 
Error using mupadengine/feval (line 157)
MuPAD error: Error: The second argument must be of form x or x = a..b. [int]

Error in solve (line 160)
  sol = eng.feval('symobj::solvefull',eqns,vars);

[Walter Roberson]

The lower limit is at V = -1 exactly, where the integral is approximately .9526391033789570 . The upper bound is V approach infinity where the integral is 5/e which is approximately 1.839397205857212

When V < -1 then the integral is infinite.

[Walter Roberson]

Notice that because the lower limit is about 0.95, it can never be 0, so there are no real-valued solutions.

[modem sudhakar]

Dear walter, I plotted the function by varying V as:

for V=0:1:10 plot(V,integral(@(x) x.^2.* exp(-x-1./(x+V)),1,inf )); hold on end

From this I can see that it is giving positive values. So, if I want get value of V for given integral value as:

solve(integral(@(x) x.^2.* exp(-x-1./(x+V)),1,inf ))==1.4,V)

From above 'for' loop the value should come as V=1. But it is giving the error as:

Undefined function or variable 'V'.

Error in @(x)x.^2.*exp(-x-1./(x+V))

Error in integralCalc/iterateScalarValued (line 314) fx = FUN(t);

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

[Walter Roberson]

You need to make the integral symbolic. Then vpasolve for V