Proble : maxima finds a primitive, but not a defnite integral.
Subject: Proble : maxima finds a primitive, but not a defnite integral.
From: Barton Willis
Date: Wed, 21 Nov 2012 11:21:23 +0000
>Could some kind soul explain to me why maxima can easly find this primitive :
>(%i1) integrate(1/(1+sqrt(x)), x);
>(%o1) 2 (sqrt(x) + 1) - 2 log(sqrt(x) + 1)
>but does not appy it to this definite integral :
>(%i2) integrate(1/(1+sqrt(x)), x, 0, 1);
Even for an integrand that is continuous on R, Maxima doesn't always find an antiderivative that is continuous on R; example:
(%i1) integrate(1/(5+cos(x)),x);
(%o1) atan((2*sin(x))/(sqrt(6)*(cos(x)+1)))/sqrt(6)
Thus Maxima needs to be circumspect about evaluating a definite integral by using the antiderivative.
--Barton