What is the antiderivative of #ln(x^3)/x#?

1 Answer
mason m
Dec 3, 2016

#3/2(ln(x))^2+C#

Explanation:

This is the same as asking:

#intln(x^3)/xdx#

Using the logarithm rule #log(a^b)=blog(a)# we can move the constant out. Then, a good substitution would be #u=ln(x)#, which implies that #du=1/xdx# (see this through taking the derivative of #ln(x)#).

#=3intln(x)/xdx=3intln(x)(1/xdx)=3intudu=3u^2/2=3/2(ln(x))^2+C#

We see that integration by parts isn't even necessary!

Related questions
See all questions in Integration by Parts
Impact of this question
5531 views around the world
You can reuse this answer
Creative Commons License