Something seems to be very wrong with floats and rat... if I replace 0.5 with (1/2), I get the correct result:
(%i1) integrate(x*x^(1/2)/(1+x)^(1/2),x,0,1);
3/2
3 log(sqrt(2) + 1) - 3 log(1 - sqrt(2)) - 2 3 log(- 1)
(%o1) ---------------------------------------------- + ----------
8 8
(%i2) expand(float(%));
(%o2) .3074767996713833
The indefinite integral also misbehaves:
(%i3) radcan(integrate(x*x^(1/2)/(1+x)^(1/2),x));
(%o3) (3 log(sqrt(x + 1) + sqrt(x)) - 3 log(sqrt(x + 1) - sqrt(x))
+ sqrt(x) sqrt(x + 1) (4 x - 6))/8
(%i4) radcan(diff(%,x));
3/2
x
(%o4) -----------
sqrt(x + 1)
(%i5) radcan(integrate(x*x^0.5/(1+x)^0.5,x));
rat: replaced -2.0 by -2/1 = -2.0
rat: replaced -3.0 by -3/1 = -3.0
5/2
(%o5) - 2 x sqrt(x + 1)
(%i6) radcan(diff(%,x));
2
sqrt(x) (6 x + 5 x)
(%o6) - --------------------
sqrt(x + 1)
Viktor
-----Original Message-----
From: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu] On Behalf Of t t
Sent: Saturday, December 31, 2011 3:33 AM
To: maxima
Subject: wrong integration
Hello, dear users!
I tried to integrate the following integral and got the negative answer. Surely the answer is wrong.
Here:
integrate(x*x^0.5/(1+x)^0.5,x,0,1)
-2^(3/2)
Thank you for your attention
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