Question

is there any easy way of knowing if integration by parts is the easiest way to solve a given product integration?

Answer 1

same way you get to carnegie hall
practice

Answer 2

so like you start recognizing patterns after a while?

Answer 3

yes

Answer 4

and some times it is just a trick, like finding the anti derivative of \(\log(x)\) for example

Answer 5

but usually you see a product, something like \(x^2e^x\) or \(x\sin(x)\)

Answer 6

u mean where u do it as an int by parts for 1logx?

Answer 7

yes

Answer 8

actually you should memorize this one
\[\int\log(x)dx=x\log(x)-x\] and the check is taking the derivative of the right hand side and see that you get the integrand. it will also show you why integration by parts work, as the backwards product rule

Answer 9

similarly for
\[\int x\sin(x)dx=\sin(x)-x\cos(x)\] derive the right, see that you get the left

Answer 10

okay i see that it is just something that will get better with time

Answer 11

good luck!