Thread: Integration by parts problem

I'm supposed to do the integral (e^x)(sinh x) by integration by parts. I'm guessing I'm supposed to do it over again until I get the negative expression of the first integral on the right side, then add it to both sides and divide the right side by 2. However, I can't seem to get the expression "negative" on the right side...

Another way to do it, would of course be to use the definition of sinh x directly. This I tried to do (attachment), but I'm still not sure if I got the right answer.

Any help? Thanks!

Originally Posted by gralla55

I'm supposed to do the integral (e^x)(sinh x) by integration by parts. I'm guessing I'm supposed to do it over again until I get the negative expression of the first integral on the right side, then add it to both sides and divide the right side by 2. However, I can't seem to get the expression "negative" on the right side...

Another way to do it, would of course be to use the definition of sinh x directly. This I tried to do (attachment), but I'm still not sure if I got the right answer.

Any help? Thanks!

It can't be done using Integration by Parts. Your way works though.

Using

... which, granted, means looking inside sinh and ignoring a much simpler way, but nonetheless...



... where (key in spoiler) ...

Spoiler:

... is the product rule, where straight lines are differentiating downwards with respect to x.



... is lazy integration by parts, doing without u and v.

(And solve the top row for I.)


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