Welcome back! Today we're continuing with integration techniques. You're making great progress. Let's pick up where we left off with integration by parts.
3:00 PMSounds good. I reviewed the notes from last session. I think I understand the formula but I'm not sure how to pick u and dv.
3:01 PMGreat question. The LIATE rule helps you choose u: Logarithmic, Inverse trig, Algebraic, Trigonometric, Exponential. Pick u from whichever comes first in that list. Let's test your understanding.
3:02 PMFor the integral of x * e^x dx, which should you choose as u?
I think it's B, u = x, because algebraic comes before exponential in LIATE.
3:04 PMExactly right! When u = x, then du = dx, and dv = e^x dx gives v = e^x. Applying the formula: integral of x*e^x dx = x*e^x - integral of e^x dx = x*e^x - e^x + C.
3:04 PMLet's try a slightly harder one. This requires applying the technique twice.
3:05 PMWhat is the integral of x^2 * sin(x) dx? Which substitution starts correctly?