See here
personally, i like my way the best (this is usually not the case)
...oh, i didn't show the full working... oh well, i gave a small outline. try it. Mr F's method is there too
There should be another thread around where this was done completely...you can do a search if you want
But if you were to do it your way
let
and math
So
and
Giving us
So for the second integral we get
Giving us a grand finale of
An easier method that might have been mentioned elsewhere would be as if you were just calculating
So for this case let
and
so then
and
So once again using our parts formula we get
Now for the second one we apply parts again and once again let dv=dx to get
as you can see your method is by far the messiest, there are very few integrals where you have
and let and
There are some I think, but they are uncommon