problem with definite integral

[Snake]

problem with indefinite integral

I think it should be an easy one, but I don't know where to start.

\(\displaystyle \displaystyle{\int\,}\)\(\displaystyle \dfrac{x^2}{\left(4\, -\, 2x\, +\, x^2\right)\, \cdot\, \sqrt{2\, +\, 2x\, -\, x^2\,}}\, dx\)

Sorry guys I made a mistake in the title. It should say indefinite integral.

 

[Deleted member 4993]

I think it should be an easy one, but I don't know where to start.

\(\displaystyle \displaystyle{\int\,}\)\(\displaystyle \dfrac{x^2}{\left(4\, -\, 2x\, +\, x^2\right)\, \cdot\, \sqrt{2\, +\, 2x\, -\, x^2\,}}\, dx\)

Sorry guys I made a mistake in the title. It should say indefinite integral.

4 - 2x + x² = (x-1)² + 3

2 + 2x - x² = 3 - (x-1)²

What do you think would be the next step now....

 

[Ishuda]

I think it should be an easy one, but I don't know where to start.

\(\displaystyle \displaystyle{\int\,}\)\(\displaystyle \dfrac{x^2}{\left(4\, -\, 2x\, +\, x^2\right)\, \cdot\, \sqrt{2\, +\, 2x\, -\, x^2\,}}\, dx\)

Sorry guys I made a mistake in the title. It should say indefinite integral.

I know WolframAlpha sometimes makes things more complicated than necessary but I'm not sure about this one
http://www.wolframalpha.com/input/?i=integrate+x^2%2F%28x^2-2x%2B4%29%2Fsqrt%282%2B2x-x^2%29