Integrating (e^x)sin(x)
First and foremost, this is an integration of two functions multiplied together and so the first thing that should come to your head is integration by parts from C4. However, when we usually do integration by parts we differentiate one function again and again till it goes to 1 and we are left with an easy integral. However, both e^x and sin(x) we can differentiate them forever and if you kept doing the same steps over and over again you would get nowhere, stuck in a loop.So what we do is, we label our integral as 'I' for example and we go through our standard steps of integration by parts so we get: I = some function + some integral till this integral is eventually also 'I'. Sub in 'I' for the the integral and then we will get our final result of: something x I = some function. I will demonstrate this integral on a whiteboard.
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