Question

Integration by parts problem

Answer 1

I have to integrate this (t-1)*cost

I know I need to use integration by parts, but I am wondering do I need to multiply out the bracket first?

Answer 2

No.

Answer 3

There is a way without multiplying out the brackets, but I believe when you multiply out the brackets you can setup two integrals, one that requires integration by parts, the remaining one being a normal integral

Answer 4

Yeah I thats what I was thinking cause I will have two products.

Answer 5

\[ \large \int t\cos (t) dt - \int \cos(t)dt \]

Answer 6

last one is easy, first one is easy too actually, because the highest exponent is of order 1 in the t, so you can get rid of it with just one integration by parts step.

Answer 7

It sounds easier If I don't multiply out the bracket at all!

Answer 8

\[t \sin(t) - \int \sin(t)dt = t \sin(t) + \cos(t) \] for the first one

Answer 9

always do what suits you the best @ironictoaster

Answer 10

Yeah I'mletting u=t-1 and dv=cost t then finding du and v with deriving and integrating and then plugging it into the integration by parts formula

Answer 11

I'm getting t*sint-sint+cost+c...