I need to integrate from 0-t. I am told to set u= Erf and u'= (2e^-x^2)/pi^1/2. v' is 1 and v=x.

i am also told that the answer is t Erf(t)+ ((e^-t^2)-1)/pi^1/2

how many times do I need to integrate by parts to come to that answer? It gets more complicated to me each time I integrate, no matter which assignments I use. Can I somehow do it keeping the Erf designation or do I need to use the actual function (which they didn't give in this assignment.)

TIA

## Comments

^{-x²}dx, can be solved with the u-substitution (no v's!):^{-x²}, du = -2x e^{-x²}⇒ ∫xe^{-x²}dx = -(1/2) ∫du = -(1/2) u = -(1/2) e^{-x²}.^{-x²}dx. This is the integration-by-parts part! :)^{-x²}, thereby avoiding a second integration by parts.