Question

Question #ccb06

Answer 1

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)`