ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 04 Jan 2017 14:44:16 -0600Two ways of integrating x↦xⁿsin(x) give contradictory results. Bug?http://ask.sagemath.org/question/36185/two-ways-of-integrating-x-xnsinx-give-contradictory-results-bug/**First way:**
var('x,n')
integral(x^n*sin(x),x)
gives just
integrate(x^n*sin(x), x)
not very informative, let us try to add an assumption to get nicer results.
**Second way:**
assume(n,'integer')
integral(x^n*sin(x),x)
gives
1/4*(((-1)^n - 1)*gamma(n + 1, I*x) - ((-1)^n - 1)*gamma(n + 1, -I*x))*(-1)^(-1/2*n)
Uhm, looks better, but... wait, isn't `(-1)^n-1` equal to `0` for even values of `n` ? That would make the whole thing equal to `0` for even `n`.
I = integral(x^n*sin(x),x)
for k in range(10):
print I.subs(n==2*k)
prints only `0`s. Weird, non-zero functions should not have zero integrals.
**Third way :**
Let us try to do the integration with particular values of `n`.
for n in range(5):
print integral(x^n*sin(x),x)
prints
-cos(x)
-x*cos(x) + sin(x)
-(x^2 - 2)*cos(x) + 2*x*sin(x)
-(x^3 - 6*x)*cos(x) + 3*(x^2 - 2)*sin(x)
Looks better, but is clearly different from the previous answer.
**Question:**
I am working on the cloud, with SageMath 7.4 kernel. Is this a bug or did I misunderstood the meaning of the `'integer'`assumption ?
If this is a bug, how should I report it, is posting this question here enough ?
P.S. I did read the [wiki page about reporting bugs](http://doc.sagemath.org/html/en/developer/trac.html#reporting-bugs), but, gosh, is it really necessary to have a google account in order to report a bug ? Both sage-devel and sage-support are on Google Groups. lbWed, 04 Jan 2017 14:44:16 -0600http://ask.sagemath.org/question/36185/How do I understand the result of symbolic integralshttp://ask.sagemath.org/question/7574/how-do-i-understand-the-result-of-symbolic-integrals/So now I know how to integrate, but when I type in
sage: deriv=diff((exp(x)-1)/x,x); deriv
e^x/x - (e^x - 1)/x^2
sage: deriv.integrate(x)
-1/x + Ei(x) - gamma(-1, -x)
why don't I get back `(exp(x)-1)/x +C `?
Philipp SchneiderWed, 18 Aug 2010 13:04:12 -0500http://ask.sagemath.org/question/7574/