What is the antiderivative of $(ln^6 x)/x$ ?

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Answer 1 · 2016-01-31T18:22:34

$(ln^7x)/7+C$

Use substitution.

Let $u=lnx$ , so $du=1/xdx$ .

Finding the antiderivative is equivalent to finding

$int(ln^6x)/xdx$

This can be rewritten as

$=intln^6x(1/x)dx$

Using the substitutions previously defined

$=intu^6du$

This is equal to

$=1/7u^7+C$

Resubstitute $u$ :

$=(ln^7x)/7+C$

What is the antiderivative of (ln^6 x)/x(ln^6 x)/x?