Basic Integration Solved: Find Antiderivative of ln(x^20)^2

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Homework Help Overview

The discussion revolves around finding the antiderivative of the function \((\ln(x^{20}))^{2}\), which falls under the subject area of integration in calculus.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster seeks guidance on which method of integration to apply, expressing difficulty in identifying a suitable approach. Other participants explore the properties of logarithmic functions and suggest reconsidering the expression for simplification.

Discussion Status

Participants are actively engaging with the problem, with some providing hints related to logarithmic identities. There is recognition of a potential oversight in the original expression, which may have contributed to the confusion. The discussion reflects a mix of exploration and clarification without reaching a definitive conclusion.

Contextual Notes

Participants mention feeling stuck and suggest that there may be a simple step or identity that has been overlooked, indicating a possible gap in understanding or application of logarithmic properties.

Lanza52
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[SOLVED] Basic Integration

[tex]\int (ln(x^{20}))^{2}dx[/tex]

Just need to find an antiderivative.

Once again, drawing a blank on the easy stuff. Could anybody tell me which method of integration to use?
 
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Hrmmm..After playing with it for a long time... I feel like a middle schooler.

Partial integration didn't help. Couldn't find a working substitution. No trigonometric etc

So that means (this is just a guess) that I'm probably missing a simple little step at the beginning that is throwing me off. Been searching through little identities and looking at examples in my textbook etc.

No luck =(

Any help would be great!
 
Um... think about the law of the log function.

ln(x^2) = ?
 
Ughh...I knew it. Forgot to change ln(x^20) into 20lnx.

All that time wasted...lol

Thanks tho!
 
Lanza52 said:
Ughh...I knew it. Forgot to change ln(x^20) into 20lnx.

All that time wasted...lol

Thanks tho!

You would have wasted more time if you didn't come here!
 

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