Evaluate: $\int e^x.\sin (x) dx$
My Attempt; $$=\int e^x.\sin (x) dx$$ $$=\sin (x).e^x - \int \cos (x).e^x dx$$ Neither of $\cos (x)$ and $e^x$ is going to vanish although we keep on using By Parts. How to procced further?
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Do parts again or complexify integral – Biggs Jan 18 '18 at 05:13
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Hint: Differentiate the trig function on the right a second time (another integration by parts), and note that you have (up to sign difference, which can be remedied by moving the sign to the outside of the integral) a copy of what you started with. you should be able to manipulate the equation to get $2\cdot$ (the integral you started with)=(stuff), and thus easily find your solution. – Justin Benfield Jan 18 '18 at 05:14