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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.