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# Integrals using u squared substitutions (e.g. u^2 = 3-x)

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1. Hi,

I am having trouble figuring out how to solve questions such as the following:

Find the integral of (2x)(sqrt(3x-4)) using the substitution 3x-4 = u^2

To me, it is much easier to substitute u = 3x-4 (and can solve for this), but the question explicitly requests u^2 = 3x - 4. I cannot even see the reasoning for using u^2as it seems to complicate rather than simplify the question.

Anyone able to explain why you would want to solve it this way? And more importantly, how to solve it?
2. (Original post by NeT_SLeePeR)
Hi,

I am having trouble figuring out how to solve questions such as the following:

Find the integral of (2x)(sqrt(3x-4)) using the substitution 3x-4 = u^2

To me, it is much easier to substitute u = 3x-4 (and can solve for this), but the question explicitly requests u^2 = 3x - 4. I cannot even see the reasoning for using u^2as it seems to complicate rather than simplify the question.

Anyone able to explain why you would want to solve it this way? And more importantly, how to solve it?
It makes a lot more sense because then the square root disappears, the square root is an ugly thing in integration. So it makes your life easier.

Anyways: .

So your integral becomes now substite to get your integral in terms of only.

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