Non-easy indefinite integral

不是不可以的。

把sin x轉換成taylor series，然後慢慢搞。

2011-12-24 11:19:17 補充：

圖片參考：http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/indefiniteintegral/madindefiniteintegral9.jpg

參考資料：
my wisdom of maths + formula from http://en.wikipedia.org/wiki/List_of_integrals_of_trigonometric_functions#Integrals_involving_only_sine + http://en.wikipedia.org/wiki/Factorial#Double_factorial + http://mathworld.wolfram.com/DoubleFactorial.html

This is not non-easy
It is impossible to do
You should know that, many integral cannot be evaluated, such as error function.

The only possible way to do that is Taylor expanion.


圖片參考：http://i44.tinypic.com/104gbwz.gif


The higher degree can make the coeff reduce. the series is the exact form of f(x) when degree of the polynomial lend to inf

Therefore, you can easily integrate this f(x)

Here is the result (taylor expansion up to x^15)


圖片參考：http://i42.tinypic.com/rh1pwk.gif



Defined integral can be very easy to handle it.
This indefinite integral seem to be useless.

http://www.wolframalpha.com/input/?i=%E2%88%AB+%28x%2B3%29%C2%B3+*+sinx+*+sin^-%28x%29+dx