Kumulsan KalkulusLogaritma Natural

D x ln x =

1 x

ln 1=0u ln =ln uln v v

1 dx=ln xCx lim x=x

ln uv=ln uln v

lim ln x=x 0

Integrasi dan Diferensiasi Trigonometri

sin x dx=cos xC cos x dx=sin xC 1 dx=sin 1 xC 2 1x 1 x dx=sin 1 C 2 2 a a x

sec2 x dx=tan xC tan x sec x dx=sec xC1 dx=tan1 xC 2 1x1 a 2 x 2 dx= 1 tan1 aln e x = x

csc 2 x dx=cot x C cot x csc x dx=csc xC e

1 dx=sec1 xC 2 x x 1 1 1 x dx= sec1 C 2 2 a a x x a=x

x C a

formula

Fungsi Eksponensial

e x 0

ln x

D x e x =e xx

e x dx=e xCa x =e xln a

e x dx =e xCln x= e log x

lim e x =

Integrasi Parsial

u dv=uv v duSifat Trigonometri

u dv=[uv ] b tot b v du aa a

b

sin 2 xcos2 x=1Sifat 2 sin dan 2 cos

1cot2 x=csc 2 x2

1tan 2 x=sec 2 x cos 2x=2cos x12

cos 2x=cos x sin x

2

cos 2x=12 sin x

2