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Math Help - integration problems

  1. #1
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    integration problems

    25.) integrate
    xsqrt(x-5) dx

    i think this is integration by parts with u = x and dv = x-5 is this correct?



    35.) integrate
    e^(2x) * sinx dx

    u = sinx dv = e^(2x)

    i end up doing integration by parts 1 time and then i find i have to do it again


    after the 2nd integration of parts i end up with.......
    (sinx)(e^(2x))-(cosx)(e^(2x)) + integral of | e^(2x)(sinx)

    the problem is the bolded part is the original equation...but when i move it to the other side it cancels out the problem...i have no idea what i am doing wrong -thx
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  2. #2
    Super Member Random Variable's Avatar
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    For the first problem, integration by parts is not needed. Just let u = x-5.

    For the second problem, you made a sign error somewhere.
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  3. #3
    Super Member Random Variable's Avatar
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     \int e^{2x} \sin x \ dx = -e^{2x} \cos x + 2e^{2x} \sin x - 4 \int e^{2x} \sin x \ dx
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  4. #4
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    k

    ok i got the second one....but the first one i still dont understand


    how can u let u = x-5...it wont make the x in the front of the problem disappear ??
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  5. #5
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    Quote Originally Posted by maybnxtseasn View Post
    [snip]
    but the first one i still dont understand


    how can u let u = x-5...it wont make the x in the front of the problem disappear ??
    Have you not been taught the technique of u-substitution?
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  6. #6
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    Quote Originally Posted by maybnxtseasn View Post
    ok i got the second one....but the first one i still dont understand


    how can u let u = x-5...it wont make the x in the front of the problem disappear ??
    If \displaystyle u = x - 5 then \displaystyle x = u + 5...
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