" !$#&%('*),+$-.#/+0-2143(%536'7#819+$!$':%7;"!$#<1="!,1/'*>/?('7@2@A'CB D4EGF(HIF7J*FLKNM*OPQSRTRVUXWYZWR[\W]_^a`bRXcedfW Z Z R Z Z Z Z Z a dx = ax + c x2 +c x dx = 2 xm+1 xm dx = +c m∈N m+1 dx 1 =− +c x 6= 0 2 x x √ dx √ = x+c x 6= 0 2 x xα+1 α x dx = +c α ∈ Q − (−1) et x 6= 0 si α < 0 α+1 dx = ln |x| + c x 6= 0 x ex dx = ex + c ax +c a > 0 et a 6= 1 ln a Z sin x dx = − cos x + c Z ax dx = Z cos x dx = sin x + c Z dx = (1 + tan2 x) dx = tan x + c cos2 x Z dx =− x+c x= 6 kπ k ∈ Z sin2 x Z %(;"1gC! D*EGF(HIF7J*FLKNM*OUTY\UXWdhdfWY Z #/i x dx = %ji x + c Z %gi x dx = #/i x + c Z 1=i x dx = ln(%gi x) + c Z Z dx %gi = (1 − 1/i x) dx = 1=i 2 2 x x sin 2x + +c 2 4 Z x sin 2x sin2 x dx = − +c 2 4 Z tan x dx = − ln | cos x| + c Z Z x 6= π + kπ k ∈ Z 2 x+c cos2 x dx = ln x dx = x ln x − x + c π + kπ et k ∈ Z 2 x>0 x 6= D*EGF(HIF7J*FLKNM*OUTY\UXWdhdfWY /Y7UT`[ W Z Z Z Z Z Z Z Z Z Z Z dx x = ln | tan( )| + c x 6= (2k + 1)π et k ∈ Z sin x 2 dx x π π = ln | tan( + )| + c x 6= + 2kπ et k ∈ Z cos x 2 4 2 1 + x 1 dx +c x ∈] − 1, 1[ = ln |x| = 6 1 1 − x2 2 1−x dx √ = − +c |x| < 1 = 2 1−x dx x +c = 1 + x2 √ dx √ = ln |x + x2 + 1| + c 2 x +1 √ dx 2 − 1| + c √ x x > 1) = ln |x + |x| > 1 x2 − 1 √ dx √ = ln |x + x2 + h| + c x2 + h > 0 2 x +h x dx = ln | ( )| + c x > 0 ou x < 0 x 2 dx =2 (ex ) + c x dx = ln | x| + c x > 0 ou x < 0 x ;+ >/%(#/-2! > C1=i #<- 9>/%(%7;# ><%(1="! ;+ 9> #<i ;"+ > %ji #<- /1 i ><%(1gC! #/i #/i g% i 1=i F J4MGE:J4FTc$]DGE:J*F(M4O Z 0 u(x) v (x) dx = u(x) v(x) − Z Z u0 (x) v(x)dx b a #%$ &GM Pc$YZc-RXW/. u(x) v 0 (x) dx = [ u(x) v(x) ]ba − Z + '(1$- ?7><'7!,1/- "!0@A'(# b u0 (x) v(x)dx a HIM' J)(XW+*0c$]_`fc, dfW a 6= 0 1 f (ax + b) + c a Z 1 (ax + b)α+1 (ax + b)α dx = + c α 6= −1 (ax + b 6= 0 si α < 0) a α+1 Z 1 dx = ln |ax + b| + c ax + b 6= 0 ax + b a Z f 0 (ax + b) dx = Pc$Y021R31] ced4. Z f 0 [u(x)] u0 (x) dx = f [u(x)] + c Z [u(x)]α u0 (x) dx = Z [u(x)]α+1 +c α+1 u0 (x) dx = ln |u(x)| + c u(x) Z b f (x)dx = a Z u(x) 6= 0 tb f [φ(t)] φ0 (t) dt ta α 6= −1 (u(x) 6= 0 si α < 0) 5 '7% ;!$;"1/;!$'6'(17$-8 ?(>/'7!51=-A"!$@2' φ6 #<+$> [t , t ] 'L1 a = φ(t ) , b = φ(t ) a b a b