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Re: Indefinate integrals, erroneus Natural log?
On 18 Jun., 13:02, "David Rees" <w3bdevilREM... at THISw3bdevil.com> wrote: > Hi, > > In preparation for a major exam tomorrow, I was just checking some of my > answers to past-papers with mathematica, I fed it this input: > > In:= > \!\(\[Integral]\((xE\^\(2 x\))\) \[DifferentialD]x\) > Out= > \!\(xE\^\(2\ x\)\/\(2\ Log[xE]\)\) > > I marked myself wrong and moved on to the next question, but I happened > accross the actual mark-scheme which said I was correct. It gave this > answer: > > ((1/2)xE^(2x))-(1/4)e^(2x) > > My Integral calculus isn't so strong, so I don't know if the additional > natural log should be there, or if the two expressions are identical. > > Thanks Hello Note that you should have a space (or a multiplication operator) between your variable x and the constant E (the base of the natural logarithm). The following input gives your expected output: In:= Integrate[x*E^(2*x), x] Out= E^(2*x)*(-(1/4) + x/2) Whereas using the variable xE gives your (not expected) output: In:= Integrate[xE^(2*x), x] Out= xE^(2*x)/(2*Log[xE]) I hope this helps. Best Regards Norbert Marxer