# Complex Integration by Parts Help. Please

## Main Question or Discussion Point

Hi
Can anyone help me with this integration.
I will use I to symbol the integer sign

Limits between 1 and 0

Ie^-x.Sinxdx

I understand I have to integrate by parts and get the following answer, ignoring the limits for the time being.

Ie^-x.Sinx = e^-x.Cosx I -Cosx.e^-x dx

then i believe i have to integrate the second part of the sum ( I -Cosx.e^-xdx)and i get.

I -Cosx.e^-xdx= -Cosx.-e^-x- I -e^-x.Sinx

Now i am stuck.
How do I combine the two answers to get a single sum which i can then put between limits.??

Thank you.

Is this what you are trying to integrate:

$$I=\int_{0}^{1}e^{-x}sin(x)dx....????$$

I dont see any complex integral here. I might be wrong as well, cuz my eyes are going...lol...

let $$u=e^{-x}, du=-e^{-x}dx,and,v=\int sin(x)dx=-cosx$$

Integrate by parts twice, and you will get sth in terms of the original integral, and you will be fine.

The OP might be referring to the integral

$$\int^{1}_{0} ie^{-x} \sin (x) dx$$

?

$$S=\int_{0}^{1}e^{-x}sinxdx.$$
This is the actual sum. Now I have learnt how to set it up properly.
Thanks

Is this what you are trying to integrate:

$$I=\int_{0}^{1}e^{-x}sin(x)dx....????$$

I dont see any complex integral here. I might be wrong as well, cuz my eyes are going...lol...

let $$u=e^{-x}, du=-e^{-x}dx,and,v=\int sin(x)dx=-cosx$$

Integrate by parts twice, and you will get sth in terms of the original integral, and you will be fine.
There is no need for subsitution here - actually I don't see how it helps, you'd get something like $\sin\log u$....not really helpful.

Just use integration by parts right away, and you'll get back to the integral you started from for which you can then solve.

There is no need for subsitution here - actually I don't see how it helps, you'd get something like $\sin\log u$....not really helpful.

Just use integration by parts right away, and you'll get back to the integral you started from for which you can then solve.
I dont see myself saying to use substitution lol....!!!!

And as long as i can see, i also suggested integration by parts, and that twice.

We might have different concepts of what substitution and integration by parts is, who knows!!!!!!!!!!!!!

OR... Probbably my eyes are really going lol.....

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Oh true you didn't mention substitution explicitly, my fault.

But why did write down then what du is .....hm, doesn't matter. I guess our concepts of subsitution and integration by parts are rather similar. Last edited:
Oh true you didn't mention substitution explicitly
Neither explicitly nor implicitly!