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Math Help - Simple Integration

  1. #1
    Newbie AmberLamps's Avatar
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    Simple Integration

    I have an integrating factor of e^(3lnt)and have simplified it to e^t^3 near the end of the problem we are required to integrate -3t^3 dt which comes to -3/4t^4 right?

    Now my friend has kept the integrating factor in the form e^(3lnt) throughout the problem and thus has to integrate -3e^(3lnt) dt at the end of the problem. She, however, thinks that this becomes -te^(3lnt).

    Obviosuly one of us is wrong; but who?
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  2. #2
    Junior Member
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    Quote Originally Posted by AmberLamps View Post
    I have an integrating factor of e^(3lnt)and have simplified it to e^{t^3} near the end of the problem we are required to integrate -3t^3 dt which comes to -3/4t^4 right?

    Now my friend has kept the integrating factor in the form e^(3lnt) throughout the problem and thus has to integrate -3e^(3lnt) dt at the end of the problem. She, however, thinks that this becomes -te^(3lnt).

    Obviosuly one of us is wrong; but who?
    If you post the problem, I could tell you for sure, but given an integrating factor of e^{3ln(t)}, I would simplify this to e^{ln(t^3)}. The log and the exponential then cancel out to give you an integrating factor of t^3. Is this the integrating factor that you actually got?

    Secondly, how did your friend get -te^{3ln(t)}? Anycase, he is wrong, if you take the super complicated and long way around, you still get the integration of \frac{e^{4ln(t)}}{4}=\frac{t^4}{4}.

    Out of interest, if you want to do the long way, let u = ln(t), hence t = exp(u) then let v =4u. Don't for get to change the dt in each case.
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