# Is this integration probelm right so far?

• Ravenatic20
In summary, there are multiple methods that can be used to solve integration problems, including substitution, integration by parts, and partial fraction decomposition. To check if your solution is correct, you can differentiate it or use online calculators or consult with a peer or mentor. While calculators can be helpful, it is important to understand the concepts and methods involved. Common mistakes to avoid include forgetting the constant of integration and making algebraic errors. To solve integration problems more efficiently, you can use shortcuts, simplify the integrand, and practice regularly. Understanding the concepts and methods thoroughly can also improve efficiency.
Ravenatic20
$$\int_{e}^{infinity} \frac{dx}{x \ln x} = \int_{e}^{infinity} \frac{1}{x \ln x} dx = \int_{e}^{infinity} \frac{1}{\ln x} d \ln x = ln|lnx| + C$$evaluated from e to infinity

I think I know what I need to do next, I just want to make sure I'm good up to this point. Also, how do you put in an infinity sign, and evaluate sign? Thanks!

Infinity is just \infty. Dunno about the other.

Anyway, it looks correct to me.

Looks right. (And divergent)

## 1. Is there a specific method that must be used to solve integration problems?

No, there are multiple methods that can be used to solve integration problems. The most common methods include substitution, integration by parts, and partial fraction decomposition. The method used depends on the complexity of the problem and personal preference of the scientist.

## 2. How do I know if my integration problem is correct?

One way to check if your integration problem is correct is to differentiate the solution and see if it matches the original function. Another way is to use online integration calculators or check with a peer or mentor.

## 3. Can I use a calculator to solve integration problems?

Yes, calculators can be helpful in solving integration problems, especially for complex calculations. However, it is important to understand the underlying concepts and methods in order to use the calculator correctly and interpret the results.

## 4. Are there any common mistakes to avoid when solving integration problems?

Yes, common mistakes include forgetting to add the constant of integration, incorrect application of integration rules, and making algebraic errors. It is important to double check your work and practice regularly to avoid these mistakes.

## 5. Are there any tips for solving integration problems more efficiently?

Yes, some tips include identifying patterns and using shortcuts, simplifying the integrand before solving, and practicing regularly to improve speed and accuracy. It is also helpful to understand the concepts and methods thoroughly to solve problems more efficiently.

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