# How to integrate something that keeps on repeating

• dwilmer
In summary, the integral of e^t (1+3sint) cannot be solved by the technique of integration by parts because the resulting terms on both sides will never be the same. The integral can be split into two parts, with the first being easily solvable and the second requiring the use of integration by parts.
dwilmer

## Homework Statement

What is integral of e^t (1+3sint)?
I tried integ by parts but its not working
Im familiar with the technique where you end up with two idental integrals on either side, then you add one side to the other, and divide by 2.
This isn't working though. Mainly because the RHS will never be same as term on LHS, because the 1 either cancels or else becomes a t, at the first integration or differentiation.

## The Attempt at a Solution

You mean

$$e^t (1+3\sin(t))$$

or

$$e^{t (1+3\sin(t))}$$

not that I will know in either case, just it is not clear to me what the question is.

dwilmer said:

## Homework Statement

What is integral of e^t (1+3sint)?
I tried integ by parts but its not working
Im familiar with the technique where you end up with two idental integrals on either side, then you add one side to the other, and divide by 2.
This isn't working though. Mainly because the RHS will never be same as term on LHS, because the 1 either cancels or else becomes a t, at the first integration or differentiation.

I suspect you mean $\int e^t (1+ 3sin(t)dt$ because Borek's suggested $\int e^{t(1+ 3sin(t)}dt$, while plausible from what you wrote, is intractible.

First, split the integral up: $\int e^t dt+ 3\int e^t sin(t)dt$. The first is easy and the second can be done by the technique you mention. One integration by parts gives a term of $\int e^t cos(t)dt$ and a second gives [itex]\int e^t sin(t)[/tex] again.

thanks Halls

## 1. How can I integrate a repeating function in my experiment?

The best way to integrate a repeating function in your experiment is to use a computer program or software that has the capability to handle repetitive tasks. This will save you time and ensure accuracy in your data analysis.

## 2. Can I use a mathematical formula to integrate a repeating pattern?

Yes, you can use a mathematical formula to integrate a repeating pattern. However, the formula may vary depending on the specific pattern or function that is repeating. It is important to consult with a mathematician or scientist to ensure the accuracy of your formula.

## 3. Is there a specific method for integrating a repeating pattern in a complex system?

There is no one-size-fits-all method for integrating a repeating pattern in a complex system. It will depend on the specific system and the type of pattern that is repeating. It is important to carefully analyze the system and consult with experts to determine the best approach.

## 4. How can I ensure that my integration of a repeating function is accurate?

To ensure accuracy, it is important to thoroughly test and validate your integration method before using it in your experiment. This can be done by comparing the results of your integration with known data or using simulations to mimic the repeating pattern. It is also helpful to have multiple scientists review and verify your integration process.

## 5. Are there any potential errors or limitations when integrating a repeating function?

Yes, there may be potential errors or limitations when integrating a repeating function. These can include computational errors, limitations of the integration method, or inaccuracies in the data. It is important to carefully consider these factors and address them in your analysis to ensure the reliability of your results.

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