# Wolfram gave me one answer, examiners gave me another

• Saibot
In summary, the conversation discusses the use of u substitution in integration and the resulting different expressions for the constant C. It is explained that both expressions are correct, as they differ only by a constant. The example of cos(2x) is given as an illustration of how different approaches to integration can yield different results.
Saibot
Homework Statement
Find the integral of 1/(2x-2)
Relevant Equations
u substitution
I removed the coefficient of 1/2 before integrating. So I had:
1/2 integral[(1/x-1)]
= 1/2 ln(x-1) + C

Using u substitution without removing the coefficient yields
1/2 ln(2x-2) + C

I get how it works both ways, and my answer must be wrong, but what exactly is causing this conflict? Am I not supposed to remove the factor of 1/2?

What is happening here?

##\ln(2x-2) = \ln(2(x-1)) = \ln(x-1) + \ln 2##
Therefore, ##\ln(x-1)## and ##\ln(2x-2)## differ only by a constant so both (divided by 2) are primitive functions of ##1/(2x-2)##.

Saibot
What is happening is that as @Orodruin explained both are antiderivatives (=indefinite integrals) of the given function, however you use in both expressions the same letter ##C## for the constant and that is what is causing the confusion. We know that ##C## can be anything so it doesn't matter if you have just ##\ln x+C## in one expression and ##\ln x+C+\ln2## in the other, because if ##C## is anything, then so is ##C+\ln2## anything.

Saibot
Got it, thanks guys. So I'm not actually wrong, we'll both just get different expressions for C.

DaveE and Delta2
Saibot said:
Got it, thanks guys. So I'm not actually wrong, we'll both just get different expressions for C.
It's happens quite often with integration. For example:
$$\cos(2x) = \cos^2 x - \sin^2 x = 2\cos^2 x -1 = 1 - 2\sin^2 x$$Any one of these may result depending on how you tackle the integral $$-2 \int \sin(2x)\ dx$$

SammyS and Saibot

## 1. Why did Wolfram give me one answer while examiners gave me another?

There are a few possible reasons for this discrepancy. One possibility is that Wolfram used a different set of data or assumptions in their calculations. Another possibility is that the examiners used a different methodology or set of criteria to evaluate your answer. It is also possible that there was an error in either the Wolfram answer or the examiner's answer.

## 2. Which answer should I trust, Wolfram's or the examiners'?

It ultimately depends on the context and purpose of the question. If the question is related to a specific exam or assignment, the examiners' answer should be considered the correct one. However, if the question is more general in nature, it may be worth considering both answers and evaluating their differences to gain a better understanding of the topic.

## 3. Is Wolfram's answer always accurate?

Wolfram's answers are based on algorithms and data that they have compiled, so they can be considered reliable. However, like any other source, they may contain errors or limitations. It is always important to critically evaluate any answer, regardless of its source.

## 4. Can I use Wolfram's answer as a reference in my research or assignments?

It is generally not recommended to use Wolfram's answer as a reference in academic work. While they may provide a good starting point for further research, it is important to use primary sources and peer-reviewed literature for references.

## 5. How can I reconcile the differences between Wolfram's answer and the examiners' answer?

If possible, it is best to consult with the examiners or your instructor to understand the discrepancies and clarify any misunderstandings. It may also be helpful to review the methodology and assumptions used by both Wolfram and the examiners to better understand the differences. In some cases, it may be necessary to do further research or calculations to reach a conclusion.

• Calculus and Beyond Homework Help
Replies
6
Views
735
• Calculus and Beyond Homework Help
Replies
5
Views
1K
• Calculus and Beyond Homework Help
Replies
2
Views
854
• Calculus and Beyond Homework Help
Replies
2
Views
965
• Calculus and Beyond Homework Help
Replies
22
Views
1K
• Calculus and Beyond Homework Help
Replies
3
Views
1K
• Calculus and Beyond Homework Help
Replies
9
Views
902
• Calculus and Beyond Homework Help
Replies
10
Views
1K
• Calculus and Beyond Homework Help
Replies
3
Views
1K
• Calculus and Beyond Homework Help
Replies
12
Views
2K