# Have i integrated this correctly?

• Dell
In summary, to check if you have integrated a function correctly, you can differentiate it and see if you get the original function back. To avoid mistakes when integrating, carefully follow integration rules, double check your work, and use online tools or software. Some common mistakes to watch out for include forgetting the constant of integration, incorrect chain rule application, and algebraic errors. It is possible to integrate a function in more than one way, but the end result should be equivalent. If you are having trouble integrating a function, you can try different techniques, consult resources, and practice regularly.
Dell
$$\int$$(x-5)/(x2-2x+2)dx

(x-5)/(x2-2x+2)=(x-1-4)/((x-1)2+1)

x-1=t therefore x=t+1

dx=x'dt=(t+1)'dt=dt

$$\int$$(x-5)/(x2-2x+2)dx=$$\int$$(t-4)/(t2+1)dt

=$$\int$$t/(t2+1)dt-4$$\int$$1/(t2+1)dt

=0.5ln|t2+1|-4arctg(t)+c

## 1. How do I know if I have integrated a function correctly?

One way to check if you have integrated a function correctly is by differentiating it and seeing if you get back the original function. If you do, then you have integrated correctly.

## 2. How can I avoid making mistakes when integrating?

To avoid mistakes when integrating, it is important to carefully follow the integration rules and steps. Additionally, double checking your work and using online integration tools or software can also help catch any errors.

## 3. What are some common mistakes to watch out for when integrating?

Some common mistakes to watch out for when integrating include forgetting to add the constant of integration, not applying the chain rule correctly, and making algebraic errors such as incorrect sign changes.

## 4. Is it possible to integrate a function in more than one way?

Yes, it is possible to integrate a function in more than one way. Some integration techniques, such as substitution or integration by parts, may lead to different forms of the same integral. However, the end result should still be equivalent.

## 5. What should I do if I am having trouble integrating a function?

If you are having trouble integrating a function, you can try using different integration techniques, consulting a textbook or online resources for examples, or seeking help from a tutor or classmate. It is also important to practice and review the integration rules and techniques regularly to improve your skills.

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