# I think my problem solving is absurd.

• stanton
In summary, the conversation discusses evaluating a definite integral using the equation \int u^n du/dx = u^(n+1)/(n+1) (n not equal to -1). The individual attempted to solve the integral but ran into an issue with the denominator becoming zero. They then asked for assistance with integrating \int \frac 1 u \, du and received guidance on using u = e^{-x} + 2 and du = -e^{-x}. After applying this substitution, the individual was able to obtain the correct answer.
stanton

## Homework Statement

Evaluate the definite integral:

## Homework Equations

$$\int u^n du/dx$$ = u^(n+1)/(n+1) (n not equal to -1)

## The Attempt at a Solution

(-1) muliplied by $$\int$$ (e^-x +2)^-1 (-e^-x) dx = ?

and if I follow the equation above, I got denominator zero, for I broke the rules 'n is not equal to zero'
I think I did as the equation. but now what should I do now?

Do you know how to integrate

$$\int \frac 1 u \, du$$
?

Let u = e^(-x) + 2
the du = ...

-e^(-x)

So with $$u = e^{-x} + 2$$ and $$du = -e^{-x}$$, what happens to your integral?

So with LaTeX Code: u = e^{-x} + 2 and LaTeX Code: du = -e^{-x} , what happens to your integral?

Thank you for your help. I did like this:

Can you check is this the right answer?

Looks good. You are correct that the absolute value signs are not needed in the answer, since $$e^{-x} + 2$$ is never negative.

## 1. What is problem solving and why is it important?

Problem solving is the process of finding a solution to a particular issue or challenge. It involves identifying the problem, gathering information, analyzing possible solutions, and implementing the best course of action. Problem solving is important because it allows us to overcome obstacles, make decisions, and achieve our goals.

## 2. How do you know if your problem solving skills are absurd?

There are a few signs that may indicate your problem solving skills are not effective. These include constantly encountering the same problems, feeling overwhelmed or frustrated when faced with a problem, and struggling to come up with viable solutions. If you feel like your problem solving is not getting you the results you want, it may be time to reassess your approach.

## 3. Can problem solving skills be improved?

Yes, problem solving skills can be improved with practice and effort. Just like any other skill, problem solving takes time and effort to develop. By actively seeking out and solving problems, reflecting on your process, and learning from your mistakes, you can improve your problem solving abilities.

## 4. What are some common mistakes people make when problem solving?

One common mistake people make when problem solving is jumping to conclusions or making assumptions without fully understanding the problem. Another mistake is being too focused on finding a single "right" solution, rather than considering multiple options. Additionally, not taking the time to thoroughly analyze the problem or rushing through the process can also lead to ineffective problem solving.

## 5. How can problem solving skills be applied in different situations?

Problem solving skills can be applied in a variety of situations, from personal matters to professional challenges. In everyday life, problem solving can help with making decisions, resolving conflicts, and managing time effectively. In a work setting, problem solving is crucial for overcoming obstacles, improving processes, and achieving goals. It is also a valuable skill in fields such as science, engineering, and technology, where finding solutions to complex problems is essential.

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