Updates:
        Status: Started

Comment #8 on issue 1188 by ondrej.certik: integrate(1/sin(x)**2,x) fails
http://code.google.com/p/sympy/issues/detail?id=1188

Thanks! First of all: many thanks for attacking this problem!

Now some technical things:

* all tests must pass, e.g. if you do "./setup.py test", it must all run.  
You can
start by fixing for example the white space failures:

$ bin/test sympy/utilities/
============================= test process starts  
==============================
executable:   /usr/bin/python  (2.5.4-final-0)

sympy/utilities/tests/test_code_quality.py[2] F.                           
[FAIL]
sympy/utilities/tests/test_decorator.py[1] .                                 
[OK]
sympy/utilities/tests/test_iterables.py[4] ....                              
[OK]
sympy/utilities/tests/test_lambdify.py[25] ...........f.............         
[OK]
sympy/utilities/tests/test_pickling.py[?]   Failed to import               
[FAIL]
sympy/utilities/tests/test_pytest.py[1] .                                    
[OK]
sympy/utilities/tests/test_tests_names.py[1] .                               
[OK]

________________________________________________________________________________
________ /home/ondra/repos/sympy/sympy/utilities/tests/test_pickling.py  
________
   File "/home/ondra/repos/sympy/sympy/utilities/tests/test_pickling.py",  
line 203, in
<module>
     from sympy.integrals.trigonometry import Cos_2k_integrate,  
Sin_2k_integrate
ImportError: cannot import name Cos_2k_integrate

________________________________________________________________________________
   
sympy/utilities/tests/test_code_quality.py:test_no_trailing_whitespace_and_no_tabs
    
File "/home/ondra/repos/sympy/sympy/utilities/tests/test_code_quality.py",  
line 63,
in test_no_trailing_whitespace_and_no_tabs
     check_directory_tree(sympy_path)
    
File "/home/ondra/repos/sympy/sympy/utilities/tests/test_code_quality.py",  
line 43,
in check_directory_tree
     assert False, message_space % (fname, idx+1)
AssertionError: File contains trailing whitespace:
/home/ondra/repos/sympy/sympy/integrals/trigonometry.py, line 58.

= tests finished: 32 passed, 1 failed, 1 xfailed, 1 exceptions in 0.70  
seconds =
DO *NOT* COMMIT!


I don't know which editor you use. I use vim and I use this to highlight  
all trailing
whitespace:

if has('gui_running')
    hi WhiteSpaceEOL guibg=#FF0000
else
    hi WhiteSpaceEOL ctermbg=Red
endif
match WhitespaceEOL /\s\+\%#\@<!$/

I am sure a similar thing can be done in every major editor.

* Then I have a comment to this:

+def sin_even_integrate(k,x):
+
+    class Sin_2k_integrate(PolynomialSequence):
+        """efficient integrate(sin(x)**2k, x)"""
+
+        @staticmethod
+        @recurrence_memo([_x])
+        def calc(k, prev):
+            """recursively calculate \int(sin(x)**2k, x)
+
...

It's not very nice to put a class inside a function etc. Let's implement  
everything
as a class, or everything as a function.

The algorithm that you propose seems simple (I like that!) so it should be  
easy to
fix it.

But otherwise it seems pretty good. It's a very good start to get this  
issue fixed.
Thanks!

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