AP Calc BC Formulas

∫ a^u du

∫ a^u du

a^u/ln a + c

∫ tan u du

-ln | cos x | + C or ln | sec x | + C

∫ cot u du

ln | sin x | + C

∫ sec u du

ln | sec x + tan x | + C

∫ csc u du

∫ -ln | csc x + cot x | + C

∫ du/√(a² - u²)

sin^-1(u/a) + C

∫ du/(a² + u²)

1/a tan^-1(u/a) + C

Integration by parts/product rule

∫uv = uv - ∫vdu

Tabular integration

u dv

p-test on ∫1, ∞ (dx/x^p)

diverges if p ≤ 1 (infinity)

1/(p-1) if p > 1

p-test on ∫0, 1 (dx/x^p)

diverges if p ≥ 1 (infinity)

converges if p < 1 :(

LIPTE

log, inv trig, polynomial, trig, exponential