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Integrate the function\[e^x(\sin x+\cos x)\]

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  • $\int e^x\{f(x)+f'(x)\}dx=e^xf(x)+c.$
Given $I=\int e^x(\sin x+\cos x).$
 
Here let f(x)=sin x.
 
Then f'(x)=cos x.
 
Clearly this of the form $\int e^x\{f(x)+f'(x)\}dx.$
 
Therefore $\int e^x(\sin x+\cos x)=e^x(\sin x)+c.$

 

answered Feb 11, 2013 by sreemathi.v
 
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