Apparently there is some error in the integrate algorithm.
Consider the following integral:
int(x/sqrt(ax+b)) which is 2*sqrt(ax+b)*(ax-2b)/(3a**2) as is easily
confirmed doing integration by parts. Many integral tables (not all) has
this integral correctly listed.
sympy 1.4 gives me this:
code (ipython 7.5.0):
In [1]: from sympy import
*
In [2]: a,b,x=symbols('a b x')
In [6]:
f=x/sqrt(a*x+b)
In [7]:
int=integrate(f,x)
In [8]:
factor(int)
Out[8]: 2*sqrt(b)*(a*x*sqrt(a*x/b + 1) - 2*b*sqrt(a*x/b + 1) + 2*b)/(3*a**2)
where clearly the last term shouldn't be there.
Hope this can help improving the integrate algorithm.
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