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Homework Help: Integrate this.

  1. Dec 5, 2006 #1
    1. The problem statement, all variables and given/known data
    Integrate [e^(-x)*sin(e^x)]dx ?

    This is part of the work. I was actually rying to find the general solution to the differential equation y"+3y'+2y=sin(e^x) using the variation of the parameter method.

    2. Relevant equations
    Particular solution Y = u1(x)y1(x) + u2(x)y2(x), where u1 and u2 are functions of x, y1 and y2 were determined from the homogeneous version of the equation.

    Wronskian = e^(-x)+2e^(-x) = 3e^(-x)

    u1 = integral of -(e^x)sin(e^x)/(3e^-x)dx = -1/3 (sin(e^x)-e^xcos(e^x))

    3. The attempt at a solution

    I don't know how to integrate u2. Is there a trick involved?
  2. jcsd
  3. Dec 5, 2006 #2


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    www.quickmath.com - powered by webMathematica: this site is very handy and will do algebra (factoring, simplify, partial fraction decomposition, expand), solve equations/inequalities (single or a system), plot equations/inequalities (single or a system), derivatives, definite or indefinite integrals, and do matrix arithmetic/inverses/determinants.
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