On Wed, Sep 11, 2013 at 10:37 AM, Ondřej Čertík <[email protected]> wrote: > Hi Peter! > > On Wed, Sep 11, 2013 at 7:19 AM, Peter Luschny <[email protected]> > wrote: >> Consider >> >> (F1) sqrt(1+x^3)/x >> (F2) sqrt(1+1/x^3)*sqrt(x) >> >> According to Mathematica's online integrator >> >> (I1) integral F1 dx = (2/3)*(sqrt(x^3+1)-arctanh(sqrt(x^3+1))) >> (I2) integral F2 dx = >> (2*sqrt(1/x^3+1)*x^(3/2)*(sqrt(x^3+1)-arctanh(sqrt(x^3+1))))/(3*sqrt(x^3+1)) >> >> SymPy Live computes (I1) as >> (S) 2*x**(3/2)/(3*sqrt(1 + x**(-3))) - 2*asinh(x**(-3/2))/3 + >> 2/(3*x**(3/2)*sqrt(1 + x**(-3))) >> >> SymPy Live timed out with (I2). SymPy 0.7.3 computes (I2) as >> (S) 2*x**(3/2)/(3*sqrt(1 + x**(-3))) - 2*asinh(x**(-3/2))/3 + >> 2/(3*x**(3/2)*sqrt(1 + x**(-3))) >> >> The derivative of (S) is (F2) and not (F1). So I am inclined to >> say that SymPy computes (I1) not correctly. > > > Thanks for reporting this. Here is what I tried: > > In [1]: x = Symbol("x", real=True) > > In [2]: f = integrate(sqrt(1+x**3)/x, x) > > In [3]: e = f.diff(x).simplify().expand().factor().cancel() > > In [4]: print e > (x**3 + 1)/(x**(5/2)*sqrt(1 + x**(-3))) > > It's kind of a pain to simplify "f", but at the end, the expression [4] is > equal > to sqrt(1+x^3)/x, as you can check by hand, at least for x > 0. > > How did you make it equal to (F2)?
F1 and F2 are equal for x > 0. Aaron Meurer > > Ondrej > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy. > For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. For more options, visit https://groups.google.com/groups/opt_out.
