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I am suppose to find $\int(\ln x)^3$ by using the proof (I have to prove this part first) of

$$\int (\ln x)^n dx = x(\ln x)^n - n \int (\ln x)^{n-1} dx$$

I can not prove it and I do not know how to work with n powers like that, to me it doesn't even look right.

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    To prove the last formula (do you see how to apply it?), try integration by parts. The $u$ and $dv$ that work are somewhat surprising; for now let me just say that if your $dv$ is hard to integrate, then you're doing too much work.2012-06-08
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    I do not understand how to do it with n as a power though, it doesn't make sense.2012-06-08
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    @Jordan: You have seen formulas like $\frac{d}{dx}x^n=nx^{n-1}$? Does that make sense?2012-06-08
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    Would it be easier to think of the case $n=3$, at first? In essence it is no easier than the general case, but the concreteness might help.2012-06-08
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    (Joke, sort of): If one is asked to prove an explicit integration formula, one way is to differentiate the "answer."2012-06-08

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