<code>
from sympy import *
import itertools as it
import operator as op
def byparts(expr,x,depth=1):
print depth
hintarr=[]
if expr.is_Mul:
for part in it.combinations(expr.args,depth):
part=reduce(op.mul,part)
rest=simplify(expr/part)
part_int=integrate(part,x)
#print part_int,rest
hint=simplify(part_int*diff(rest,x))
integral=rest*part_int
hintarr=hintarr+[(hint,integral)]
hintarr=hintarr+[(x*diff(expr,x),x*expr)]
return(dict(hintarr))
def integrate2(expr,x,depth=1):
if expr.is_Add:
for part in expr.args:
rest=simplify(expr-part)
for depth in range(1,len(part.args)+1):
byparts_dict=byparts(part,x,depth)
#print rest, list(byparts_dict)
if rest in byparts_dict:
return(byparts_dict[rest])
<\code>
On Wednesday, July 11, 2012 1:23:01 PM UTC-4, pallab wrote:
>
> simple by parts integral can not be done:
>
> integrate(diff(x*f(x),x),x)
>
>
> also can not do simple integral like:
>
> integrate(diff(x*sqrt(sin(x)),x),x)
>
>
> best,
>
> Pallab
>
>
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