Possible error in Sage

asked 2015-09-11 12:19:33 -0600

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Dear all, while trying to calculate the integral of:

integrate (xe^(2x-(x^2)/2), x)

I got this:

1/2Isqrt(2)(-2Isqrt(pi)(x - 2)(erf(sqrt(1/2)sqrt((x - 2)^2)) - 1)/sqrt((x - 2)^2) + Isqrt(2)e^(-1/2(x - 2)^2))e^2

Which is actually wrong.

The answer is simply e^x²



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Are you sure about your statement ? The derivative of e^(x^2) is 2*x*e^(x^2), which seem not equal to your first function.

tmonteil gravatar imagetmonteil ( 2015-09-11 14:11:28 -0600 )edit

yeah the function you first stated is x*(e^(2x-(x^2)/2)) which is not equal to e^x^2, also (according to sage) the integral of your stated function is what you stated and for e^x^2 the integral is -sqrt(pi)i/2 * erf(ix)

Chernoxyl gravatar imageChernoxyl ( 2015-09-13 17:21:15 -0600 )edit