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Math Help - integration by parts question

  1. #1
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    integration by parts question

    can someone solve

    ∫9xcos(3x+1)dx
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  2. #2
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    Quote Originally Posted by cummings15 View Post
    can someone solve

    ∫9xcos(3x+1)dx
    = 9x∫cos(3x + 1)dx - ∫d/dx (9x) ∫cos(3x + 1)dx dx
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  3. #3
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    integration

    Hello,

    Define the functions f(x)=9x and g(x)=\cos(3x-1).

    Choose which function you would like to integrate and which one you would like to diferentiate. Then simply apply the formula:

    \int f(x)g(x)= F(x)g(x)-\int F(x)g'(x)
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  4. #4
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    Quote Originally Posted by cummings15 View Post
    can someone solve

    ∫9xcos(3x+1)dx

    tabular integration ...

    sign ....... u ............ dv .....

    (+) .........x ........... 9cos(3x+1)

    (-) .........1 ........... 3sin(3x+1)

    ..............0............-cos(3x+1)

    \int 9x\cos(3x+1) \, dx = 3x\sin(3x+1) + \cos(3x+1) + C<br />
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  5. #5
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    Unhappy

    Quote Originally Posted by surjective View Post
    Hello,

    Define the functions f(x)=9x and g(x)=\cos(3x-1).

    Choose which function you would like to integrate and which one you would like to diferentiate. Then simply apply the formula:

    \int f(x)g(x)= F(x)g(x)-\int F(x)g'(x)
    It would not be wise to choose 9x as the function to integrate.

    The order in which the first(to differentiate) and second(to integrate) functions should be taken is

    Inverse Trigonometric
    Logarithmic
    Algebraic
    Trigonometric
    Exponential
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  6. #6
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    integration

    Hello,

    The functions I defined were not meant to be fixed. You could just swop them around. I just wanted the basic idea to be understood, i.e. that you may choose either one of the function to integrate or differentiate, ofcourse selecting wisely.
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  7. #7
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    Quote Originally Posted by surjective View Post
    Hello,

    The functions I defined were not meant to be fixed. You could just swop them around. I just wanted the basic idea to be understood, i.e. that you may choose either one of the function to integrate or differentiate, ofcourse selecting wisely.
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  8. #8
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    thanks skeeter
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