From galactus,. It helped me verifying my result and confirmed it.
I got that the derivative of .
While from Mathematica, it gives the result which I doubt is equal to my result. Can you confirm my result (if yes, I will think that the result from Mathematica is the same, even if it seems more than incredible.). Thanks!!
I don't think that you should use the formula given by galactus if any one of the limit is constant.suppose if both limits were constant then you would have got 0 as result which is not necessary.
Since you were solving definite integral getting you can not take even constant for granted as we do in indefinite integral(giving general term e.g c for all constant terms) but in definite integral showing constant term is must.
I don't understand all what you mean, but the formula galactus gave works here. (Now I realize I proved it about 9 months or so ago.) And if both of the limit of the integral were constants, say 0 and 10, then the derivative would be 0, which is true. Think about it, you have . It's obvious that the integral is equal to a constant, whatever x is, since it doesn't depends of x. So the derivative of F is 0 (since the derivative of a constant is always 0).I don't think that you should use the formula given by galactus if any one of the limit is constant.suppose if both limits were constant then you would have got 0 as result which is not necessary.
Since you were solving definite integral getting you can not take even constant for granted as we do in indefinite integral(giving general term e.g c for all constant terms) but in definite integral showing constant term is must.
If I typed it well, I got that the derivative equals . It surprises me more and more. If somebody has Mathematica and has some time to spend, I'll be glad if you could check out the derivative of the integral!One way to check this would be to let a = 0, say, and then put Mathematica on the job. Note that there are various equivalent forms of the correct answer.