Integration by parts. Ive been studying for my final exam tomorrow in calc and iv seen two formulas for integration by parts. The one my teacher gave me is int_{?}^{?}[F'(x) * G(x)dx = int_{?}^{?} [F(x) * G(x)]'dx - int_{?}^{?} F(x) * G'(x) dx.

But iv also been watching some videos on youtube teaching this and most of them use the formula int_{?}^{?}udv = uv - int_{?}^{?} vdu. Are they both the same or do they have different uses?

Question

Integration by parts.  Ive been studying for my final exam tomorrow in calc and iv seen two formulas for integration by parts.  The one my teacher gave me is int_{?}^{?}[F'(x) * G(x)dx = int_{?}^{?} [F(x) * G(x)]'dx - int_{?}^{?} F(x) * G'(x) dx.

But iv also been watching some videos on youtube teaching this and most of them use the formula int_{?}^{?}udv = uv - int_{?}^{?} vdu.  Are they both the same or do they have different uses?

anonymous · Answer

sry every time you see int_{?}^{?} it is supposed to be integral.  I thought it would work

anonymous · Answer

They are the same, as $$ \int \frac{d[F(x) G(x)]}{dx}dx = F(x)G(x)$$which is the same as the uv part done in other videos.

anonymous · Answer

k thats awsome.  Cause i really like the udv equation better

anonymous · Answer

Indeed, it's quite clearer :-)