How to integrate e^x cos(x) using parts?

In summary, the conversation discusses the possibility of integrating e^x (cosx) and the confusion that arose while attempting to do so. The solution is suggested to integrate by parts twice, resulting in a non-circular answer. Another method using deMoivre's theorem is also mentioned.
  • #1
Firepanda
430
0
Is it possible to intergrate

e^x (cosx)

i wondered because i tried to intergrate it by parts, but ended up going round in circles.

I wondered because i had this question and I am stuck on how to do it :)

http://img505.imageshack.us/img505/320/frfbc8.png
 
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  • #2
Sure it's possible. Just integrate by parts twice. You will get back to where you started - but if you call the integral I, then you will get I=somthing-I. So I=something/2. Not circular. On the other hand the question you posted is done more directly with deMoivre. cos(x)+j*sin(x)=e^(j*x).
 

Related to How to integrate e^x cos(x) using parts?

1. How do I choose which function to integrate and which function to differentiate?

When using integration by parts, it is important to choose one function to differentiate and one function to integrate. A helpful tip is to choose the function that becomes simpler after differentiation as the first function, and the function that becomes more complex after integration as the second function. In this case, e^x is the simpler function after differentiation, so it should be the first function, and cos(x) is the more complex function after integration, so it should be the second function.

2. How do I know when to stop integrating by parts?

Typically, integration by parts should be repeated until the resulting integral is either solvable or reduces to a simpler form. In some cases, this may require multiple repetitions of the integration by parts formula. If the integral becomes more complex after each repetition, it is recommended to stop and try a different method.

3. Do I need to rearrange the terms before integrating by parts?

No, the order of the terms does not matter when using integration by parts. However, it may be helpful to rearrange the terms to make the process easier or to follow a specific pattern.

4. Can I use integration by parts to solve definite integrals?

Yes, integration by parts can be used to solve definite integrals. After integrating by parts, the limits of integration should be applied to the resulting integral. This will give the final value of the definite integral.

5. Are there any other methods to solve this type of integral?

Yes, there are other methods to solve integrals involving products of exponential and trigonometric functions. Some other methods include substitution, trigonometric identities, and integration using a Taylor series expansion. It is important to explore and understand different methods to determine the most efficient approach for a specific integral.

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