Question #ccb06

1 Answer
MetaPhysik
Dec 23, 2017

Correction:
#int(x(cosx-sinx)^2)/(cosx+sine)dx#

can not be integrated and expressed in commonly known functions.

Explanation:

It is not clear whether the integration is
1. #int ((cosx-sinx)^2dx)/(cosx+sinx)# or
2. #int (x(cosx-sinx)^2dx)/(cosx+sinx)#

Either way, use the identity

Correction, an error is identified in above identity

#cancel((a-b)^2= (a-b)(a+b)#

It should be #a^2-b^2 = (a-b)(a+b)#

Hence the following solutions are not long valid.

  1. #int ((cosx-sinx)^2dx)/(cosx+sinx)#
    = #cancel(int ((cosx-sinx)(cosx+sinx)dx)/(cosx+sinx)#
    = #cancel(int (cosx-sinx)dx)# = #cancel( int d(sinx+cosx)#
    = #cancel (sinx + cosx + c #

  2. #int (x(cosx-sinx)^2dx)/(cosx+sinx)#
    = #cancel (int x(cosx-sinx)dx)#
    = #cancel (int x d(sinx+cosx)#

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