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Math Help - True or false?

  1. #1
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    Question True or false?

    True or false?

    ∫4xe^2x dx = (2x-1)e^2x+c.Justify your answer.





    I think it isn't true.

    =4∫x dx + ∫e^2x dx
    =4.1 + e^2x +c
    =4+e^2x+c

    Am I doing it right?Can somebody pls suggest something?
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  2. #2
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    Quote Originally Posted by mathcalculushelp View Post
    True or false?

    ∫4xe^2x dx = (2x-1)e^2x+c.Justify your answer.





    I think it isn't true.

    =4∫x dx + ∫e^2x dx
    =4.1 + e^2x +c
    =4+e^2x+c

    Am I doing it right?Can somebody pls suggest something?
    The two terms are multiplied together, not added. You cannot break them up and integrate separately like you tried.

    The method you need to use is integration by parts. Are you familiar with it? Another way to check without actually integrating is to differentiate the proposed solution they gave and see if it matches up as it should.
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  3. #3
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    Question By parts method?

    Okay I tried differentiating it by the product rule and got the ans.Could you pls tell me how to do it by parts method?
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  4. #4
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    Quote Originally Posted by mathcalculushelp View Post
    Okay I tried differentiating it by the product rule and got the ans.Could you pls tell me how to do it by parts method?
    \int udv = uv-\int vdu

    That is the formula behind this method. u and v are the two functions being multiplied. You have to choose which one to call u and which to call v though. Many times only one combination will work out so that you can solve the problem. For this one you have 4x and e^(2x), which one should be u and which should be v?
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