Intergrate sin3x dx

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1. If (e^x)(sin3x)=Im ((e^x)(e^i3x))integrate (e^x)(sin3x) I get the answer(e^x)(cos3x-3sin3x) +C My book gets the answer
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2. y = e^2xsin3x Find the derivative.So I used the product rule and I got sin3x(e^2x)+cos^3x(e^2x). But the actual answer is
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3. given (e^x)sin3x = Im((e^x)(e^i3x)) Integrate (e^x)sin3x.dxYou can just take the imaginary part of the integral of
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4. Prove By induction that sinx + sin3x + sin5x +.... Sin(2n-1) =sin^2(nx)/sin3x
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