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The intergral for cosx is sinx, but '2x' must be considered.

When differentiating a sinx/cosx function, the '2x' would be differentiated separately

and placed in the front (multipling). So w...

This is a 'quadratic in e^x'. The easiest way to recognise this when starting problems like this is to let y=e^x. As you practice problems like this, you will find yourself moving away from this step. But...

This sort of question is quite common, and a little bit complicated, so the explanation is quite long! But it's a great one to understand. There are a few tricks you need to know to be able to do...