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# Integrating by substitution watch

1. 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
2. (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.
3. (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?
4. (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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