Hi i am completely stuck trying to integrate the following function.
f(x) = (x + 2)(1 - e^ -x/3).
Do i try and expand the brackets before i start?
I tried doing it as a substitution using 1-e^-x/3 as u and
du = 1/3 e^ -1/3x but that isn't one constant away from the original function when i multiply.
Any help would be brilliant.
(Sorry DeMath, if this is far from what you had in mind! But anyway...)
Just in case a picture helps...
(As usual, straight lines differentiate downwards or integrate up.)
The essence of integration by parts is to work backwards through the product rule for differentiation...
... we want to fill out this product-rule shape usefully, but starting in one of the bottom corners instead of - as happens in differentiation, the top one. Choosing the right arrangement can be tricky, but once you've started in the right way, as above, it's really a matter of following through. Fill in the rest of the product-rule shape, then you'll need to cancel the addition you just entered, to make the lower equals sign valid, again.
Don't integrate - balloontegrate!
Balloon Calculus Forum
Yeah i have done a bit of it but i think i was making the problem over complicated! went back to my books to recap on method after you sent the steps to make sure i understood it. Think i was confusing it with integration by substitution. Thanks for your help!