sin x.lncos xdx.. sin x.tan xdx..[r]
(1)2 4 dx x x 1 2 sin x(sin x 1)dx cos x x x 1 dx x2 1 cot x1 ln(sin x ) dx ( x 1)dx x6 1 1 dx x2 sin x cos 4 dx sin x x dx ( x 1) x 3dx x2 1 (3x 3)dx ( x 1)( x 3x 1) e x ln x dx x x ln x x dx x 1 x ln(1 x ) dx x 1 sin xdx sin x cos x (e x e x ) ln(e x e x ) dx e x e x ln e dx x ( x 1) x x e e 1 dx (6 x x 1)(24 x 10) dx xdx 1 dx cos x (1 3x)sin xdx (2 x 3)2 dx x ln e 2 cos xdx cos x x dx ex 32 x 3 x 2dx 1 dx ( x 2)( x 1) x s inx dx cos x e3 x dx x e 1 x dx x s inxdx ( cos2 x cos2 x )dx x 64 sin xdx cos x 4dx 4x x 1 x 2 x dx x (4 x x 1) dx x3 e ln x x x ln x dx x e x cos x dx ( x3 3x x 8) dx 1 x2 x 2 sin x(sin x cos x)dx (2) 2 sin x(sin x 2cos x) dx dx x x 1 x3dx x2 1 xdx x2 sin x (sin x 4cosx )dx x3 dx 1 x2 dx ( x 1)( x 2) ( x 1) dx 3x x dx x x2 1 dx x2 13 x dx 2x 1 dx x x2 x ln x x dx x 1 e2 ln x dx e x ln x 1 2x ln dx 2 x 14 x dx sin x cot x sin x cos x I dx sin 2x tan x I dx tan x /3 sin x sin x K dx /6 sin x I 3 I 4 tan x cot x dx x 1 x dx (2cot x 5) dx 3tan x dx sin x.cos xdx 0 1 1 cos x dx 2 (2cos x 3sin x )dx ( x tan x)dx 1 x2 1 xdx x10 cos x 4 cos x dx 3 sin x dx x 1 x dx sin x sin x cot x dx sin x sin x dx dx x x sin cos 2 cot x dx ( x x)dx x2 1 (3) e ln x ln x dx x 2 cos x sin xdx x3 dx 1 x2 x cos x sin xdx 38) x sin x dx 01 sin x n (1 sin x) cos xdx(n N ) x (1 x ) dx x x .e ln(e 1)dx ln(cos x ) dx sin x sin x 4 dx sin x 4 cos x(1 sin x) dx sin x e ln x ln x dx x e 1 dx 0 2 x 1 dx sin x dx cos x cos x(sin x cos cos xdx x 16 x e x) dx dx 2 x dx x x dx 4sin x 1 cosx dx x dx 2x e2x e x dx 3 x2 dx x x 4 x dx x (x 4) dx x x dx x dx 1 e e ln x x(ln x 1)dx e x e x dx (1 2x)(1 3x 3x ) dx (x 3) x 6x dx e tan x 2 cos x x dx e 4 sin 2x dx x 1 x x 9 dx 1 sin x x 1 dx x x 1 ln x e 1dx e sin(ln x) dx x (4) 1 dx 2x e 2x e x dx ln sin xdx ln x ln x dx x 1 e x x3 dx 1 e2x 3dx x e 1 dx dx sin x cot x 3 x (x 1) dx x 1 dx 3 3x 1 2 tan x cot x 2.dx ln ex (e x 1)3 ln e 2x dx e 1 x sin x.sin 2x.sin 3xdx x 1 x8 2x dx dx e cos(ln x)dx 4 cos 2x(sin x cos x)dx x dx x 1 cos 2x dx 2 x x dx 1 x 1 x ln xdx 2x x(e x 1)dx e x 1 dx 3 3x 0 4cos x 3sin x 4sin x 3cos x dx x sin dx ln(1 x) x dx 2 (1 x ) dx dx cos x sin x.cos xdx x x ln cos x dx x2 dx (x 1) x 3 ( cos x sin x )dx x xdx x dx 2x 2 x sin x sin x cos x dx x dx x 1 (5) e e 3ln x ln x dx x ln(x x)dx 2 e (ln x) dx ln x x dx e x dx e 2 1 cos(ln x)dx ln(sin x) cos x dx x 1 dx x 1 dx x e2 cos x 6 5sin x sin x dx x 2x x dx 1 sin xdx ln(x x 1) dx 1 3 x sin x 1 cos2 x dx x sin xdx x.sin x cos xdx x ln(1 )dx x 2 sin xdx ln( x x)dx x3 x 16 dx 3 x dx 4 cos x sin xdx cos 2x 1dx x 1 2x dx 1 x ln(x 1)dx sin 2x dx 1 ( ln x ln x )dx e 3 2 ln x dx ln x dx 4 x sin xdx 1 2 x cos xdx x (x 2)2 dx 0 e ln x dx (x 1) e x e (x 1)(4 x 1) dx 2x e sin xdx 1 x x.ln x dx (6) /4 2014 xdx sin 2x.cos e2 cos (ln x)dx sin x.ln(cos x)dx cos x dx 1 x x e dx cos3 x dx 0 x dx sin 2x 1 cos x dx x 6x dx x (x 1) dx sin x (tan x 1)2 cos5 x dx 1 2x 8x 26 dx 5 sin 2x (2 sin x)2 dx 1 e sin x .sin x cos xdx x 4x dx 2x x (x 1)(x 3x 2) dx sin x (sin x 3) dx sin x.tan xdx cos x cos x dx 1 4x x dx sin x x 3 dx sin x dx cos x 0 x x dx 1 2 4x x dx 1 cos x sin x cos x dx x (x 4) sin x 9cos x dx 1 cos x.sin x dx 1 3cos x dx 3 sin 2x dx (x 4x 3) dx 4sin x 1 cos x dx x (x 1) dx x xdx 4x (x 1) dx 2 x 2x 2x dx x 4x 13 dx (7) e 3e x e e 2x dx x ln x dx ln x dx e 3e 4x e 2x x 2ex (x 2)2 dx e sin x dx dx (1 x) ln x dx 2x x 9x x 9 dx dx x e sin xdx x sin xdx cos x cos x sin x dx 0 1 0 2 x cos xdx 2 x sin x dx x cos x sin x dx e x(2 ln x) dx cos x dx x cos x dx e x e sin 2x 1 sin x dx ( x x ) dx 3 2 (x x) ln x dx e 3x e sin 4x dx 1 1 x ( ln x ln x )dx e ln x x dx x ln x dx x cos x sin x dx dx sin x dx 2 x ln(1 x ) dx x cos x.ln(1 cos x) dx x1 ( ) dx 1 x 2 e e sin 2x sin x sin x cos3 x dx x.tan x dx 1 cos x dx ln x (x 1)2 dx x 6x dx (8) x 3x x dx 1 x (x 1) dx 1 x 1 x dx e 15 x x dx ln x dx sin x (e cos x)cos x dx e 1 sin 2x sin x dx 3cos x tan x 2 cos x cos x dx ln(1 x) x dx dx x 1 x x x dx x e e x dx sin 2x.cos x cos x dx x 2x dx sin 2x 1 cos x dx x 1 dx x2 1 e2x e x dx x sin 3x cos x dx 3 0 x3 1 x 2 x 1 sin 2013 x sin 2013 x cos 2013 x dx sin x cos2 x dx e ln x (x 1)2 dx x 4 x dx e 4 x dx x x dx ex x dx x 2 2 x 1 x 1 x dx 2 cos x.cos 4x dx ln(1 x) x dx 2sin x sin 2x dx dx 1 x 5 4 sin x.ln(1 cos x) dx dx x 1dx 2 x2 dx 1 x ex 1 e x dx 0 ln 3 (cos x sin x) dx (9) x 1 dx x 3 sin 2x 3 sin 2x(1 sin x) dx x sin x cos xdx sin x (1 cos x)e x dx 2 x x2 x2 x2 dx dx sin x 1 sin x dx x 1 dx 3 3x cos x dx cos 2x x 1 dx 3 3x dx 2 x sin x.cos xdx cos 2x sin x.cos x cos x dx cos x cos x cos xdx sin 2x 2 sin x dx cos3x x x2 2 dx 4x x 3x dx x (x 1) dx x x 9 dx ln( x a x)dx 1 sin 2x sin x 2cos x dx dx x x2 dx 2 cos x dx cos 2x 1 x2 dx x2 x (1 x ) dx cos x sin x dx sin 2x cos x (1 e x ) dx 2x 1 e cos x cos x sin x x (1 x) dx 0 2x (1 x) e dx x 1 dx 3x 2 (1 x)x dx cos x cos x cos xdx (10) sin x tan xdx x 1 cos x e dx (1 x ) dx 0 (4 x ) dx 1 x5 x(1 x ) dx 2 x.tan xdx sin x sin x cos 2x dx cos x 1 sin x dx 3x x 2 sin x cos6 x dx dx sin x cos x dx x (1 x ) dx 2 sin x cos x dx sin x cos x sin x cos x dx 1 ex x dx a x dx dx x 1 (x 1) ln x dx 1 4x x 2x x dx sin x dx x sin x cos x(1 cos x) dx sin x cos x sin x cos x dx 0 sin x cos x cos x dx sin x x 2x 10x x 2x dx x 1 x dx 1 1 x 1 x2 dx 2 (3 2x) x (2x 1)3 dx x ln(x 1) dx x3 (x 1)3 dx 12x 4x x ln(x x ) 1 x 3x x 2x dx 1 dx dx x x dx (11) cos x sin x dx sin 2x cos x dx cos 2x cos x sin xdx 3 (cos x sin x)dx 0 2 4 cos 2x(sin x cos x)dx 2 cos x dx x 1 x 3 dx 2 x x 1 dx dx sin x sin x dx cos x cos x dx cos x (1 cos x) dx 2 sin x dx 3 cos x dx sin x cos x sin x dx dx dx 0 3 e2x dx e 2cos x sin x dx 3x 1 dx cos x 1 x 2 cos x dx sin x 3x dx ln (cos x) dx 11 x 1 tan x 1 x tan x dx x3 x3 x 1 x cos x sin x cos x dx tan x cos x cos x dx sin x dx cos x sin x x2 x2 dx 3x 6x 1dx sin x cos x sin x dx 1 dx x (e 1)(x 1) cos3 x cos 3cos x dx tan x dx (12) 3 cot x dx tan x dx sin x cos x dx 2 tan x dx tan x tan x dx 0 cos 2x 1 cos 2x dx e4 x dx x3 1 1 1 x cos2 (ln x 1) dx e ln(1 tan x)dx dx sin x cos x 4x dx 04x 42 x (x 1).sin 2xdx dx 2x 4x e x ln xdx 2 (2x 1).cos xdx 2x dx 2x x (e 1) e dx x 16 dx x x log2 x 1 x dx 1 x 1 dx x x 2 1 1 ex ln x x3 dx x4 10 dx x x e ln x dx x ln x sin x.tan xdx sin x cos x dx tan x e dx x x3 sin x 1cosx dx ln cos x cos 2x dx sin x.cos2 x /2 cos x cos x dx sin x cos x x 2 I dx x 1 e3 ln x dx x ln x 1 x x 1 dx x2 x.sin x dx 2x cos (13) cos x 4sin x dx cos x sin x 3sin x cos x dx 3sin x cos2 x 2x dx 01 x x 1 dx 3x 2x x sin x dx cos x 2 x x sin x dx cos x ln(tan x)dx sin x dx cos x sin x sin x ln tan x dx cos x x ln( x x ) dx (5 x 1) x ax dx a a x ; với a > x 2m dx (1 x ) m 2 sin x cos x dx (4 cos x 3) cos xdx (1 sin 3x ) n (1 sin x) cos xdx(n N ) 1 x2 dx x ln 1 x2 ( x 1)dx x x 1 sin x x cos xdx e 0 m N x.tan xdx ( x 4)dx x 3x sin n1 x cos xdx n n ; (n Z ) cos x sin x x sin x dx cos x x2 1 dx x e x 2 b a x dx; a, b (a x ) 2n (1 x n ) m dx x m, n N 4 sin x dx cot x cos x ln x 2x 2e e xdx (14)