Essential Anti-derivatives

Anti-Derivatives to memorize for Calc 2

∫xⁿ dx =

1/(n+1) ⋅ xⁿ⁺¹ + C

∫1/x dx =

ln |x| +C

∫sinx dx =

-cosx + C

∫cosx dx =

sin x + C

∫sec²x dx =

tan x + C

∫secx tanx dx =

secx + C

∫csc²x dx =

-cot x + C

∫secx cotx dx =

-cscx + C

∫tanx dx =

ln |sec x| + C

∫secx dx =

ln|secx + tanx| + C

∫cotx dx =

ln |sin x| + C

∫cscx dx =

ln |cscx - cotx| + C

∫e^x dx =

e^x + C

∫b^x dx =

(b is a constant > 0)

b^x/(lnb) + C

∫1/√(1-x²) =

sin^-1(x) + C

∫-1/√(1-x²) dx =

cos^-1x + C

∫1/(x² + a) dx =

(1/√a) tan^-1(x/√a) + C

∫sinhx dx =

coshx + C

∫coshx dx =

sinhx + C

∫lnx dx =

x ln x - x + C