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C3 integration question

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    Integrate by parts: 2x(x-2)4 dx

    I tried using the formula uv - integral (v - du/dx dx) but cant seem to do the second integral that I get?
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    (Original post by IDontKnowReally)
    Integrate by parts: 2x(x-2)4 dx

    I tried using the formula uv - integral (v - du/dx dx) but cant seem to do the second integral that I get?
    It's \int{u \frac{dv}{dx} dx} =uv - \int{v \frac{du}{dx} dx}

    What have you done so far?
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    (Original post by NotNotBatman)
    It's \int{u \frac{dv}{dx} dx} =uv - \int{v \frac{du}{dx} dx}

    What have you done so far?
    Thats what I meant, my bad!

    This is what I have:

    (x-2)^4 * x^3 - integral (x^2 * 4(x-2)^3 dx)
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    (Original post by IDontKnowReally)
    Thats what I meant, my bad!

    This is what I have:

    (x-2)^4 * x^3 - integral (x^2 * 4(x-2)^3 dx)
    One of your  v terms are wrong. The bits in bold should be the same.
    If you let \frac{dv}{dx} = 2x then integrate to get v

    Then you can integrate by parts again a few times over.
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    (Original post by NotNotBatman)
    Your  v terms are wrong. The bits in bold should be the same.
    If you let \frac{dv}{dx} = 2x then integrate to get v
    so v = x^2 ?

    I still can't do the second integral though
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    (Original post by IDontKnowReally)
    so v = x^2 ?

    I still can't do the second integral though
    Integrate by parts again. There will come a point when it's easier to expand than to do IBP.
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    (Original post by NotNotBatman)
    Integrate by parts again.
    I tried to integrate the second integral and got this:

    1/3 * (x-2)3 * x3 - integral(x3 * (x-2)2 dx)

    Now I cant integrate the one above
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    (Original post by IDontKnowReally)
    I tried to integrate the second integral and got this:

    1/3 * (x-2)3 * x3 - integral(x3 * (x-2)2 dx)

    Now I cant integrate the one above
    expand and integrate as normal. And you've factorised the 4 right?
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    (Original post by NotNotBatman)
    expand and integrate as normal. And you've factorised the 4 right?
    Oh I see, thank you.
    how do you know when it is appropriate to expand and then integrate, and when to integrate by parts/substitution?
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    (Original post by IDontKnowReally)
    Oh I see, thank you.
    how do you know when it is appropriate to expand and then integrate, and when to integrate by parts/substitution?
    When it's easier expand and integrate using add 1 to power and divide by new power rule. If the highest power is 2 of a composite function, then it'd probably be easier to expand, but if there were higher powers then use IBP. With a lot of practise, it becomes a bit more obvious.

    I usually consider integration by recognition and then using a u - sub and then by parts.
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    (Original post by IDontKnowReally)
    Oh I see, thank you.
    how do you know when it is appropriate to expand and then integrate, and when to integrate by parts/substitution?
    I think there are other methods for doing that question that are much simpler- if you do u and dv/dx the other way around in the first stage you only have to do integration by parts once, and no expanding brackets is needed.
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    (Original post by NotNotBatman)
    When it's easier expand and integrate using add 1 to power and divide by new power rule. If the highest power is 2 of a composite function, then it'd probably be easier to expand, but if there were higher powers then use IBP. With a lot of practise, it becomes a bit more obvious.

    I usually consider integration by recognition and then using a u - sub and then by parts.
    Thats really helpful, thank you (it wont let me upvote you tho :/)
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    (Original post by IDontKnowReally)
    Thats really helpful, thank you (it wont let me upvote you tho :/)
    No worries as the poster above said, swapping the u and dv would make it easier, but it's good practice to try a number of methods, then you'll quickly notice the which method to use in the future.
 
 
 
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