How do you integrate $int ln^(6)x/x dx$ ?

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Answer 1 · 2015-06-08T00:41:53

First, notice that you can rewrite this as:

$int ln^6x/xdx = int (lnx)^6*1/xdx$

Now you can see that we can do u-substitution.

Let:
$u = lnx$
$du = 1/xdx$

$int (lnx)^6*1/xdx = intu^6du$

$= u^7/7 + C$

$= ln^7x/7 + C$

How do you integrate int ln^(6)x/x dxint ln^(6)x/x dx?