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

Answer 1

Ezekiel Alexander

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

Make use of a substitute.

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

Determining the antiderivative is the same as determining

#int(ln^6x)/xdx#

This could be rephrased as

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

Making use of the previously specified substitutions

#=intu^6du#

This is comparable to

#=1/7u^7+C#

Resubstitute #u#:

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

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Answer 2

Paisley Johnson

The antiderivative of ( \frac{\ln^6(x)}{x} ) with respect to ( x ) is ( \frac{\ln^7(x)}{7} + C ), where ( C ) is the constant of integration.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.