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    Do you make u the part of the integral with the lowest power (if that makes sense??).

    E.g. if you have to integrate....

    (x^2)sin(x^3)

    you make u = x^2
    and not sin(x^3)

    Thanks
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    (Original post by kiiten)
    Do you make u the part of the integral with the lowest power (if that makes sense??).

    E.g. if you have to integrate....

    (x^2)sin(x^3)

    you make u = x^2
    and not sin(x^3)

    Thanks
    No in this case you would substitute u = x^3. You shouldn't be thinking about "highest power". What you should notice is that x^2 is a constant away from the derivative of x^3 so you substitute the thing that is being differentiated i.e. u = x^3.

    Or if you had (2x^4)sin(x^5) you would substitute u = x^5 for the same reason but if you had e.g. (2x^3)sin(x^5), substitution wouldn't work because you don't have a function/derivative pattern.

    Try carrying out the substitution and you'll see why this process only works when you have a function and its derivative.
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    (Original post by Notnek)
    No in this case you would substitute u = x^3. You shouldn't be thinking about "highest power". What you should notice is that x^2 is a constant away from the derivative of x^3 so you substitute the thing that is being differentiated i.e. u = x^3.

    Or if you had (2x^4)sin(x^5) you would substitute u = x^5 for the same reason but if you had e.g. (2x^3)sin(x^5), substitution wouldn't work because you don't have a function/derivative pattern.

    Try carrying out the substitution and you'll see why this process only works when you have a function and its derivative.
    so how do i know what to make u - is there a general rule?

    What do you mean by function/derivative pattern?
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    (Original post by kiiten)
    so how do i know what to make u - is there a general rule?

    What do you mean by function/derivative pattern?
    If you have f(something) multiplied by the derivative of "something" (or a constant away from it) then you can substitute u = something.

    E.g. x^3sin(x^4)

    The derivative of x^4 is 4x^3 which is a constant away from x^3 so you have this pattern which means you can substitute u = x^4. But it wouldn't work if you had e.g.

    x^2sin(x^4)


    But this is only one way you can use substitutions. There are many other ways but they don't all follow the same rule.
 
 
 
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