Is it mathematically sound to do this

[brandy]

apply integration by parts twice and swapping the u and v's and then rearranging the equation to say that it is equal to bla/2

like for example i said u is x^n or something and v' is sin x or something.
later on when I am faced with another integral, i apply the int by parts but this time the v' is nx^(n-1) and u is -cos x
then i rearangged the equation to say the initial integral is equal to this...

(these u's and v's are NOT the values i had in the equation AND I REALISE THIS DOESNT WORK HERE, i just want to know if the process is sound. because if so, i will be very happy haha)

 

[tiny-tim]

hi brandy!

(try using the X² icon just above the Reply box )

yes that's perfectly valid

for example ∫ sinⁿx dx = [-cosx sin^n-1x dx] + (n-1)∫ cos²x sin^n-2x dx …

use cos² = 1 - sin², and put like terms together