from
http://www.math.utexas.edu/pipermail/maxima/2011/027256.html
On Dec. 31, 2011, t t wrote:
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>*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)*--------------------------------
As mentioned by Toth and Fateman, using 1/2 instead
of 0.5 leads to the correct answer (at least numerically).
A convenient way to prepare the integrand
is to use radcan (or ratsimp):
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(%i1) exf : x*x^(0.5)/(1+x)^(0.5);
(%o1) x^1.5/(x+1)^0.5
(%i2) integrate(%,x,0,1);
(%o2) -2^(3/2)
(%i3) float(%);
(%o3) -2.828427124746191
(%i4) exr : radcan(exf);
(%o4) x^(3/2)/sqrt(x+1)
(%i5) integrate(%,x,0,1);
(%o5) (3*log(sqrt(2)+1)-3*log(1-sqrt(2))-2^(3/2))/8+3*log(-1)/8
(%i6) expand(float(%));
(%o6) 0.30747679967138
(%i7) ratsimp(exf);
(%o7) x^(3/2)/sqrt(x+1)
-----------------------------------
Ted Woollett
****************************************************************
(%i1) S:'integrate(x^(3/2)/sqrt(x+1),x,0,1)$
(%i2) changevar(S, y=sqrt(x), y, x);
"Is "y" positive, negative, or zero?"p;
(%o2) 2*integrate(y^4/sqrt(y^2+1),y,0,1)
(%i3) ev(%, nouns);
(%o3) (3*asinh(1)-sqrt(2))/4
(%i4) float(%);
(%o4) 0.307476799671383
Aleksas D
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