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Calculus

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Evaluate the integral e^x sin4x dx.

I know the answer is 1/17 e^x sin4x - 4/17 e^x cos4x + C but I don't know how to solve it out.

  • Calculus - ,

    Use integration by parts:

    I=∫exsin(4x)dx
    =exsin(4x)-4∫excos(4x)dx
    =exsin(4x)-4excos(4x)-16∫exsin(4x)dx
    =exsin(4x)-4excos(4x)-16I
    Solve for I to get the above results.

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