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

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In summary, the conversation revolved around finding an antiderivative for the function ln(x^20)^2. The individual tried using partial integration and substitution, but had no success. Eventually, they realized that they needed to convert ln(x^20) into 20lnx and were able to solve the problem with this simple step. The conversation concludes with the realization that seeking help saved them from wasting more time.
  • #1
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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  • #2
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!
 
  • #3
Um... think about the law of the log function.

ln(x^2) = ?
 
  • #4
Ughh...I knew it. Forgot to change ln(x^20) into 20lnx.

All that time wasted...lol

Thanks tho!
 
  • #5
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!
 

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

What is integration?

Integration is a mathematical operation that involves finding the antiderivative of a given function. It is the inverse process of differentiation and is used to find the area under a curve or to solve certain types of equations.

What is an antiderivative?

An antiderivative, also known as an indefinite integral, is a function that when differentiated yields the original function. It is denoted by the symbol ∫ and is often used in integration problems.

How do I find the antiderivative of a function?

To find the antiderivative of a function, you can use integration techniques such as substitution, integration by parts, or the power rule. These methods involve manipulating the given function to simplify it into a form where the antiderivative can be easily evaluated.

What is the antiderivative of ln(x^20)^2?

The antiderivative of ln(x^20)^2 is xln(x^20)^2 - 20x + C, where C is the constant of integration. This can be found by using the power rule and the chain rule for differentiation.

Can integration be used in real-life applications?

Yes, integration is used in various real-life applications such as calculating the area under a curve in physics, determining the amount of medication in a patient's bloodstream in medicine, and analyzing stock market trends in finance. It is a powerful tool in solving problems that involve continuously changing quantities.

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