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)
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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)
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Ted Woollett