BC-Only: Integration by Parts
For AB students: this is a preview of what BC adds. For BC students: essential.
Formula: ∫u dv = uv - ∫v du
LIATE rule for choosing u:
Logarithmic → Inverse trig → Algebraic → Trig → Exponential
Pick u from earlier in this list. Let dv be the rest.
Example: ∫x·eˣ dx
u = x, dv = eˣ dx. du = dx, v = eˣ.
= xeˣ - ∫eˣ dx = xeˣ - eˣ + C
Other BC topics to know: Series (Taylor/Maclaurin), parametric equations, polar coordinates, improper integrals, logistic growth. These add significant content to the AB foundation.
Reference:
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