- #1
DigiDigi
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Integration of ln(x + x^2) is it (1+2x)/(x+x^2)?
Can you integrate ln(x + x^2) using integration by parts?
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In summary, integration of ln(x + x^2) is typically solved using integration by parts and can also be simplified by factoring out the logarithm.
- #2
CompuChip
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There's always an easy check: differentiate the result.
It should give you ln(x + x²) back.
It should give you ln(x + x²) back.
- #3
tiny-tim
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Hi DigiDigi! 
If you mean differentiation, then yes that's the correct application of the chain rule.
(What is worrying you about that?)
DigiDigi said:
If you mean differentiation, then yes that's the correct application of the chain rule.
(What is worrying you about that?
)- #4
Curious3141
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DigiDigi said:
Are you trying to differentiate or integrate?
If it's the former, that's correct.
If it's the latter, it isn't. But it's easy to do. Hint: ln(ab) = ln a + ln b. Factorise!
- #5
DigiDigi
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I try to integrate. Looks like I make mistake and differentiate it. We integrate using integration by parts?
- #6
Curious3141
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DigiDigi said:
Yes. The standard way to integrate ln x is to use integration by parts. Do you know how to do this?
But first, do what I said in the previous post to split the logarithm up.
Related to Can you integrate ln(x + x^2) using integration by parts?
1. What is the formula for integrating ln(x + x^2)?
The formula for integrating ln(x + x^2) is ∫ln(x + x^2) dx = xln(x + x^2) - 2x + C.
2. What is the process for integrating ln(x + x^2)?
The process for integrating ln(x + x^2) involves using the substitution method, where u = x + x^2 and du = (1 + 2x)dx. This allows us to rewrite the integral as ∫ln(u) du, which can be solved using the formula ∫ln(x) dx = xln(x) - x + C.
3. Can ln(x + x^2) be integrated using any other methods?
Yes, ln(x + x^2) can also be integrated using integration by parts or partial fractions, depending on the form of the integral. However, the substitution method is the most commonly used and efficient method for this integral.
4. Is there a specific range of values for x that can be used when integrating ln(x + x^2)?
There are no specific restrictions on the values of x that can be used when integrating ln(x + x^2). However, it is important to note that ln(x + x^2) is only defined for positive values of x, as the natural logarithm function is undefined for negative values.
5. How can integrating ln(x + x^2) be applied in real-life situations?
Integrating ln(x + x^2) can be applied in various fields of science and engineering, such as in the study of population growth, radioactive decay, and chemical reactions. It can also be used in economics and finance to model and analyze natural growth processes.
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