Integration by Parts: Integrate e^{ax} * sin(bx) with respect to x

[Aminta_1900]

Integrate with respect to x

e^ax * sin bx

I'm getting lost somewhere, and I think it might be where I am adding to both sides.

My workings


Here I give up, because it doesn't look like the answer.


But thanks a lot for your time.

 

[apple2357]

I think you have done all the hard work already? Just tidy up step 5

what is 1/b^2 divided by (1+ a^2/b^2) ?

 

[Steven G]

Integrate with respect to x

e^ax * sin bx

I'm getting lost somewhere, and I think it might be where I am adding to both sides.

My workings

View attachment 36478
Here I give up, because it doesn't look like the answer.

View attachment 36480
But thanks a lot for your time.

simplify 1+ a^2/b^2. Hint: 1 = b^2/b^2

 

[Aminta_1900]

I think you have done all the hard work already? Just tidy up step 5

what is 1/b^2 divided by (1+ a^2/b^2) ?

Got it, thanks a lot.


I'm sure I tried this, but it must be where I lost my bearings (or mind!) and didn't try again.