Hi,
is this a Mathematica problem, or do you just need the solution to this particular exercise? If it is a Mathematica problem, note that all functions like Integrate or Sin or Cos start with a capital letter. Arguments are given in square brackets. You also will need to specify what the integration variable is.
If you type:
?Integrate
you obtain a nice description of how integrate works, i.e. the syntax.
So you might expect something like this to work better:
Integrate[x^2/(x Sin[x] + Cos[x])^2, x]
Mathematica itself does not give you the step-by-step solution. But if you type a double equal sign at the beginning of the input cell and then the integral above, you get a nice interface
It says "step-by-step" solution, so you might want to click this. This is how it is usually done. In this particular case you will encounter a problem.
Cheers,
Marco