Mastering Integrals: Solving a Tricky ln(x) Integral Problem

In summary, to solve a tricky ln(x) integral problem, one must use integration techniques and have a good understanding of logarithm properties and derivatives. Calculators cannot solve these types of integrals and a general approach is to identify the integral as a logarithmic function, use integration techniques, and then solve the remaining integral. Common mistakes to avoid include not applying the chain rule and not simplifying the integral. To improve skills in mastering ln(x) integrals, regular practice, reviewing properties and techniques, and seeking help can be beneficial.
  • #1
nitroracer
4
0
I have an integral I want to work out that should be a simple one but I just can't see where to start with it. Any help would be appreciated.

[tex]

\int\frac{lnx}{x-8xln^2x}

[/tex]
 
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  • #2
Write it as:
[tex]\frac{1}{2}\int\frac{2\ln(x)}{x}\frac{dx}{1-8\ln^{2}(x)}[/tex]
 
Last edited:
  • #3
i haven't done it but it looks like trig substitution might work
 
  • #4
Substituting for ln^2(x) works even better..:smile:
 

1. How do I solve a tricky ln(x) integral problem?

To solve a tricky ln(x) integral problem, you will need to use integration techniques such as integration by parts or substitution. You will also need to have a good understanding of the properties of logarithms and their derivatives.

2. Can I use a calculator to solve ln(x) integrals?

No, calculators are not able to solve integrals involving logarithms. These types of integrals require manual solving using integration techniques.

3. What is the general approach for solving ln(x) integrals?

The general approach for solving ln(x) integrals is to first identify the integral as a logarithmic function. Then, use integration techniques such as integration by parts or substitution to simplify the integral. Finally, solve the remaining integral using integration rules and properties.

4. Are there any common mistakes to avoid when solving ln(x) integrals?

One common mistake to avoid when solving ln(x) integrals is forgetting to apply the chain rule when using substitution. Another mistake is not simplifying the integral before solving it, which can make the solution more complicated than it needs to be.

5. How can I improve my skills in mastering ln(x) integrals?

The best way to improve your skills in mastering ln(x) integrals is to practice regularly. You can also review the properties of logarithms and their derivatives, as well as common integration techniques. Additionally, seeking help from a tutor or online resources can also be beneficial.

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