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Here is my code:

f0[x_]: =1/(E^(x^2/2)*Sqrt[2*Pi])

f1[x_]: =(Sqrt[2]*(Pi/2 + ArcTan[x]))/(E^(x^2/2)*Pi^(3/2))

K[x_]: =Integrate[f0[y]^(1 - x)*f1[y]^x, {y, -Infinity, Infinity}]

H[x_]: =Integrate[f0[y]^(1 - x)*f1[y]^x*Log[f1[y]^x/(f0[y]^x*K[x])], 
{y, -Infinity, Infinity}]/K[x]

I would like to Plot $H[x]$ for $x\in[0,1]$. However I couldnt do it. I dont need so nice figure. A rough shape is enough.

When I typed

Plot[H[x], {x, 0, 1}]

I got

Integrate::ilim: Invalid integration variable or limit(s) in {-y,-\[Infinity],\[Infinity]}. >>
And many other errors.

Could you please help me to solve this issue?

Thanks alot.

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Don't use capital letters as custom function names unless you know what you're doing. K is a reserved name. –  Jens Mar 18 '13 at 22:49
    
This seems like it's not really gonna be much use to future users and you got it (almost) right on your own. I am inclined to flag it so that it gets closed if you agree? –  gpap Mar 18 '13 at 22:51
    
as gpap says, seems a minor oversight on your part. I've voted to close (as you've got your answer). –  acl Mar 18 '13 at 22:53
    
thanks. You are all so kind. please go ahead with closing. Thanks again for the help. –  Seyhmus Güngören Mar 18 '13 at 23:04
    
@SeyhmusGüngören Btw, a final comment. Before you try plotting your integral H[x] next time, you should first look at it, because then you would have seen, that Integrate cannot calculate it. –  halirutan Mar 18 '13 at 23:39
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closed as too localized by acl, Jens, Sjoerd C. de Vries, halirutan, rm -rf Mar 18 '13 at 23:53

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1 Answer

up vote 2 down vote accepted

I replaced your syntax so that the := are all in one piece and I changed both Integrate to NIntegrate and I got a result. The usual caveat of it being better to not use variables starting with a capital letter so as not to accidentally confuse a built-in function applies.

Clear[K, H, f0, f1]
f0[x_] := 1/(E^(x^2/2)*Sqrt[2*Pi])

f1[x_] := (Sqrt[2]*(Pi/2 + ArcTan[x]))/(E^(x^2/2)*Pi^(3/2))

K[x_] := NIntegrate[f0[y]^(1 - x)*f1[y]^x, {y, -Infinity, Infinity}]

H[x_] := NIntegrate[
   f0[y]^(1 - x)*f1[y]^x*Log[f1[y]^x/(f0[y]^x*K[x])], {y, -Infinity, 
    Infinity}]/K[x]

and

Plot[H[x], {x, 0, 1}]

Mathematica graphics

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