(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This is only an example but I do not understand what they are doing...

[tex] \int (4x+1)^{3} + (4x+1)^{2}+(4x+1) dx [/tex]

2. Relevant equations

[tex] \int f(u) du = F(g(x)) + C [/tex]

3. The attempt at a solution

Let

[tex] u = 4x+1 [/tex]

then

[tex] du = 4 dx [/tex]

and

[tex] dx = \frac {1}{4}du [/tex]

how did they get that dx was 1/4? There are no steps to explain this, it just lists them as having that value.

So after substituting the problem should look like this:

[tex] \int (u^{3} + u^{2} + u) * \frac {1}{4} du [/tex]

which is this:

[tex] \frac{1}{4}(\frac{u^{4}}{4} + \frac {u^{3}}{3} + \frac {u^{2}}{2}) + C [/tex]

[tex] \frac{1}{4}[\frac {(4x+1)^{4}}{4}+\frac{(4x+1)^{3}}{3}+\frac{(4x+1)^{2}}{2}] +C [/tex]

So I suppose the only portion that I really don't understand is how they got the 1/4 dx value out of seemingly nothing....

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# Homework Help: Indefinite Integration by exchange of variables

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