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Math Help - Intergrals ( u SUB ) ... Part to part

  1. #1
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    Intergrals ( u SUB ) ... Part to part

    hey guys i recently joined, after seeing how helpful this site is =]
    i have a test tommorow and i cant figure out these review problems
    hope you guys can help thanks in advance

    integral cos(5x)cos(sin(5x)dx
    u- Sin(5x)

    teacher gave U.

    Integral 2x^2 sin (3x) DX

    teacher said this one is part to part.. and we use a table method?
    i was absent for this part of the lesson.. its said to make the problem easier to do or something?



    intergral Sin^2(x)DX

    intergral e^x sin(x)Dx
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  2. #2
    MHF Contributor matheagle's Avatar
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    on integral Sin^2(x)DX, use the half angle trig equation
    sin^2 u= (1/2)(1-cos(2u))

    For integral e^x sin(x)Dx do PARTs twice
    The trick is to keep the u and dv the same for both integrations
    and then add the integral to the other side and solve for it.
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  3. #3
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    thanks i sort of understand it..
    ive been absent to the class due to a broken hip from football and i feel like its piling up on me and cant seem to catch up on my work.

    integral cos(5x)cos(sin(5x)dx
    u- Sin(5x)

    any idea on this that one?


    thanks guys, its 3:30am here and my head is like dead.. im lookin thur all my notes and it doesnt seem to go anywhere.. sigh. fml =[
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  4. #4
    MHF Contributor matheagle's Avatar
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    you have the substitution right in front of you

    integral cos(5x)cos(sin(5x))dx
    u- Sin(5x)

    let u=Sin(5x) then du =5cos(5x)dx
    and the integral becomes [cos(u)](1/5)du
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  5. #5
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    What about the othe cos
    There is two
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  6. #6
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    can any1 tell me the answer? i cant seem to get it.
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  7. #7
    Newbie iebi's Avatar
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    \int cos(5x)(cos(sin(5x)))dx
    Let u=sin(5x) \implies du=5cos(5x)dx \implies (1/5)du=cos(5x)dx
    cos(5x)dx will be replaced by (1/5)du, so it will look like
    \int (cos(sin(5x))) \frac{1}{5} du
    Since you let u=sin(5x), the sin(5x) inside that cos(sin(5x)) will become cos(u). Bring the 1/5 into the front.
    \frac{1}{5} \int (cos(u)) du
    The integral of cos(u) is sin(u)+C
    Now plug back in the u, and your answer should be
    \int cos(5x)(cos(sin(5x)))dx = \frac{1}{5} sin(sin(5x))+C
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