Status: Valid
Owner: ----
Labels: Type-Enhancement Priority-Medium Solvers Integration
New issue 3859 by [email protected]: dsolve-based integrator for integrals
with derivatives of undefined functions
http://code.google.com/p/sympy/issues/detail?id=3859
From https://github.com/sympy/sympy/pull/2146#issuecomment-18799916. A way
to compute integral(diff(f(x)*g(x), x), x).
There is also a way to do it with dsolve. Let h(x) =
Integral(diff(f(x)*g(x), x), x). Then differentiate both sides, and solve
the differential equation in f(x). Then, solve the result for h(x).
In [4]: solve(dsolve(diff(f(x)*g(x), x) - h(x).diff(x), f(x)), h(x))
Out[4]: [-C₁ + f(x)⋅g(x)]
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