Improper integrals

Please choose a function (for the predefined cases the interval is [0,∞[)
f(x) = x/(x4+1) [0,∞[ , exact=pi/4
f(x) = 1/((4*x2 + 2*x + 1)*sqrt(x)) [0,∞[ , exact = pi/sqrt(6)
f(x) = 1/sqrt(2*exp(x) - 1) [0,∞[ , exact = pi/2
f(x) = exp(-(4*x2 - 2*x))*x2 ]-∞, ∞[ , exact = (3/32)*sqrt(pi)*exp(0.25)
f(x) = dlog(1 + x2)/(1 + x2) [0,∞[ , exact=pi*ln(2)
f(x) = sin(0.1*x)/sqrt(x) [0,∞[ , exact=sqrt(5*pi)
f(x) = (sin(x)/x)2 [0,∞[ , exact=pi/2
f(x) = x3/sinh(x) [0,∞[ , exact=pi4/8
A function of your own Please type the evaluation program of your function here using FORTRAN rules. Your final statement must be
      fu= some expression you computed before or just here depending on x
You may use the constants pi, e(=exp(1)), sqrt2(=1.414...), the integer variables i,j,k, the logicals bool1,bool2,bool3 and the double precision variables sum,h1,h2,h3,h4,y(100),z(100),a(100,100) which are all intialized with zero resp. .false. . The routine has the parameters x (double, input) and fu (double out). never change x!. first is a local integer and set 0 before calling the function the first time. You may use this in order to initialize some local data and set it 1 afterwards to avoid multiple such initialization. Your settings of the local variables are preserved during program execution.


Please choose the interval with the bound b:
[b,∞[
]-∞,b]
with b =
]-∞,∞[

Please specify your desired relative and absolute precision
epsrel = Important : 1E-12 <= epsrel <= 1E-2 !
epsabs = Important : 1E-16 <= epsabs <= 1E-6 !

Click on "evaluate", in order to submit your input.

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18.02.2015