Toán full 2019 ver 2

ĐẠI SỐ 10 Lớp toán thầy Dũng Ngõ 13, Khuất Duy Tiến ĐT: 0972026205 HDedu - Page HDedu - Page HDedu - Page HDedu - Page HDedu - Page HDedu - Page HDedu - Page HDedu - Page HDedu - Page HDedu - Page 10 www.tuhoc.edu.vn P(x) dx, Q(x) Bài toán 1: 1)(x P(x) Q(x) a A x B x1 x x2 0) P(x) Q(x) a A x x0 a A x x1 B , (x x )2 – x2)(x – x3) thì: B x C x2 1)(x P(x) Q(x) a A x x1 x a A x x1 x x3 , – x2)2 thì: B x2 1)(x P(x) Q(x) , 1)(x P(x) Q(x) – x2 C , (x - x )2 + mx + n) thì: Bx C , x mx n htttp://tuhoc.edu.vn/blog HDedu - Page 311 www.tuhoc.edu.vn VD6: Tính nguyên hàm sau: (a) I1 2x dx; x 3x 2x dx x 3x (b) I2 = HD (a) – Ta có: 2x x 3x 2 2x (x 1)(x 2) A B x A(x 2) B(x 1) (x 1)(x 2) x x A B dx (A B)x (2A B) (x 1)(x 2) A B 2A B I1 x x dx x dx 3ln|x+1| ln|x+2| + C (b) – Ta có: 2x x 3x 2x (x 1)(x 2)2 A(x 2)2 (A B)x A B 3(x 1) 3(x 2) (x 2) C (x 2)2 B(x 1)(x 2) C(x 1) (x 1)(x 2)2 (4A B C)x 4A (x 1)(x 2)2 A B (x 1) 4A B C 4A 2B C I2 A 1/3 B C 1/3 3 (x 2B C 2)2 dx dx dx dx 3 x x (x 2)2 1 ln | x | ln | x | 3 (x 2) C htttp://tuhoc.edu.vn/blog HDedu - Page 312 www.tuhoc.edu.vn Tính nguyên hàm sau: 2x dx, x 5x 5x dx, 2x 4x I1 I3 4x dx x 6x 3x dx x 3x I2 2 I4 Tính nguyên hàm sau: 2x dx, x 5x2 6x x2 2x dx, x3 x 5x I1 I3 I2 I4 x3 x3 P(x) dx, Q(x) Bài toán 2: P(x) Q(x) x 2x dx 2x 5x x2 3x dx 2x 5x P1 (x) , Q(x) R(x) P1 (x) P(x) dx Q(x) P1 (x) dx Q(x) R(x)dx x5 VD7: Tính nguyên hàm sau: I 2x 4x3 x2 2x dx = HD x5 x3 I htttp://tuhoc.edu.vn/blog x4 2x 4x3 x2 2x 2x 2 x + 2x – 4x3 + cho x x3 2x 2x x 2x 2x dx x2 2x ln x ln|x - 2| C HDedu - Page 313 www.tuhoc.edu.vn Tính nguyên hàm sau: I1 x2 x3 dx, 2x I2 x3 2x 10x dx x 2x Tính nguyên hàm sau: I1 x5 3x3 dx, x2 x I2 x3 4x dx, x2 2x I3 x 5x dx 2x htttp://tuhoc.edu.vn/blog HDedu - Page 314 www.tuhoc.edu.vn e2x I1 +C I2 ln x ln x I3 sin(2x I4 I7 x cos 2x x sin 2x I2 I2 ln x x2 I1 x2 I2 I3 x2 x3 6 ln x C cos x C ln x 2 x3 2x 2x 2x ln x 3x 11x x 1 2x xe 2x e C I4 x ln x x C x I4 ln x 14 ln x I3 11 ln x I4 ln x 5ln x C C ln x ln x C C 2(x 1) C C C 4x ln x I3 ln x C 2x 3ln x x4 I1 ln x 1)100 C I3 C 12 C x 3 ln x I2 ln x 4ln x I1 I2 cos2x C ln x I1 sin2x C C 4) (x2 200 I8 I1 cos(3x-1)+C I6 C 8(x C ) C cos x I5 C 49 ln 2x 16 C htttp://tuhoc.edu.vn/blog HDedu - Page 315 HDedu - Page 316 www.tuhoc.edu.vn sin2 x cos2 x 1 cos 2x sin2 x cos 2x cos2 x 3sin x sin 3x 3cos x cos 3x cos3 x sin3 x Tính nguyên hàm: T1 = (sinx)n dx – T1 (sin x)n dx (sin x)2k dx (sin2 x)k ( cos x) dx (1 cos2 x)k d(cos x) T1 (sin x)n dx VD1: Tính nguyên hàm: T = HD T sin2 xdx 2)k (1 t2 )k dt, sin2 xdx cos 2x dx dx x htttp://tuhoc.edu.vn/blog cos 2xdx sin2x C HDedu - Page 317 www.tuhoc.edu.vn VD2: Tính nguyên hàm: T sin3 3xdx = TOPPER Chú ý T sin3 3xdx 3sin3x sin 9x sin3xdx cos 3x VD3: Tính nguyên hàm: T sin5 ( 3x)dx cos 9x 36 C sin5 ( 3x)dx = HD Ta có: T sin9xdx sin5 3xdx sin4 3xd(cos 3x) (1 cos2 3x cos4 3x)d(cos 3x) (1 cos2 3x)2d(cos 3x) d(cos 3x) cos2 3xd(cos 3x) cos 3xd(cos 3x) cos 3x cos3 3x cos5 3x C 15 htttp://tuhoc.edu.vn/blog HDedu - Page 318 www.tuhoc.edu.vn Tính nguyên hàm: T2 = (cosx)n dx – T2 (cos x)n dx (cos x)2k dx (cos2 x)k (sin x) dx (1 sin2 x)k d(sin x) T2 (cos x)n dx 2)k (1 t2 )k dt, VD4: Tính nguyên hàm sau: T cos 3xdx = HD T 1 (1 cos 6x)2 dx (1 cos 6x 4 1 1 cos12x x sin6x dx 12 1 1 x sin6x x sin12x C 12 96 1 x sin6x sin12x C 12 96 cos 3xdx VD5: Tính nguyên hàm: T (sin8 x cos 6x)dx cos8 x)dx = HD 8x sin8 x cos8 x + cos8 (sin4 x cos x)2 cos 4x cos2 4x 16 htttp://tuhoc.edu.vn/blog 2sin4 x cos x sin 2x cos 4x 16 1 cos 4x 1 cos 8x cos 4x 16 16 35 cos 8x cos 4x 64 16 64 (1 cos 4x 32 cos2 4x)2 HDedu - Page 319 www.tuhoc.edu.vn I cos 8xdx 64 sin8x 512 cos 4xdx 16 sin 4x 64 35x 64 35 dx 64 C T3 = sinf(x).cosg(x)dx [ sin(a b) sin(a b)] cos a cosb [ cos(a b) cos(a b)] sina sinb [ cos(a b) cos(a b)] sina cos a VD6: Tính nguyên hàm sau: (a) T1 cos 3x cos 5xdx (b) I cos x sin 2x cos 3xdx = HD (a) (cos 8x cos 2x) 1 (cos 8x cos 2x)dx sin 8x 2 cos3x.cos5x = T1 sin2x C (b) Ta có: cos x.sin 2x cos 3x htttp://tuhoc.edu.vn/blog T2 cos 6x 24 (sin3x sin x) cos 3x (sin3x cos 3x cos 3x.sin x) 1 [ sin 6x (sin 4x sin 2x)] 2 = (sin 6x sin 4x sin2x) cos 4x 16 cos 2x C HDedu - Page 320 www.tuhoc.edu.vn tannxdx, dx cos2 x dx sin2 x dx cos (ax b) dx sin (ax b) tan x C cot x cot nxdx (n C ) tan(ax b) C a cot(ax b) C a VD7: Tính nguyên hàm: (a) T1 = (b) T2 = (1 tan x)dx tan xdx = HD (a) Ta có: T1 = tan xdx sin x dx cos x d(cos x) cos x ln|cosx| C (b) Ta có: T2 = TOPPER Chú ý dx cos2 x tan x C VD8: Tính nguyên hàm: (a) T1 cách làm hoàn toàn (1 tan2 x)dx (b) T2 tan2 xdx tan3 xdx = HD Ta có: T1 tan2 xdx [(tan2 x 1) 1]dx (tan2 x 1)dx dx tan x x C (b) Ta có: T2 tan2 x tan xdx [(tan2 x 1) tan x (tan2x 1) tan xdx tan xd(tan x) tan x]dx tan xdx tan xdx tan2 x ln|cosx| C htttp://tuhoc.edu.vn/blog HDedu - Page 321 www.tuhoc.edu.vn Tính nguyên hàm sau: T1 (2sin3x T2 T3 cos 2x)dx, T7 sin2x.coxdx, sin2 (1 2x)dx T8 sin x cos 2x sin3xdx sin4 2xdx, T9 (1 cot2 x)dx, sin3 (2x 1)dx, T4 T10 cot3 2xdx sin5 (1 2x)]dx, T11 tan4 2xdx, cos3 3x sin3 ( 2x)]dx T12 cot (1 3x)dx T5 [3x T6 [ Tính nguyên hàm sau: T1 cos 2x(sin4 x cos4 x)dx T2 sin3 x.sin3x.dx T3 (sin6 x cos6 x)dx T4 cos x(cos x cos3 x)dx Tính nguyên hàm: (a) T1 (sin x cos x)dx sin x cos x (b) T2 cos 2xdx sin x cos x (b) T2 tan5 xdx (b) T2 sin x.sin 2x cos 5xdx Tính nguyên hàm: (a) T1 sin2 x dx Tính nguyên hàm: (a) T1 sin(x (c) T3 cos2 x cos 2xdx (d) T4 cos3 x.cos5xdx (e) T5 sin2 x cos2 2xdx (f) T6 sin x cos x(1 cos x)2 dx )(2 sin 2x)dx htttp://tuhoc.edu.vn/blog HDedu - Page 322 www.tuhoc.edu.vn T1 cos3x+2sin2x+C T2 1 x sin(2 - 4x)+C T3 1 x sin2x+ sin4x+C 32 T4 1 cos(2x-1)- cos3 (2x 1)+C T5 x3 1 cos(2x-1)+ cos2 (2x-1) cos5 (2x-1)+C 2 10 T6 1 1 sin3x+ sin3 3x+ cos2x - cos3 2x+C 6 T7 1 cos3x - cos x+C T8 x T9 cot x+C T10 T11 T12 sin 4x cos2 2x tan3 2x sin 6x sin2x +C ln sin 2x +C tan 2x cot3 (3x 1) x +C cot(3x 1) x+C T1 sin 2x 16 sin6x+C 48 T2 sin 2x 16 sin 4x 32 T3 x+ sin4x+C 32 T4 sin x sin x 1 x+ sin6x+C 48 sin x 3x sin 2x sin 4x +C 32 htttp://tuhoc.edu.vn/blog HDedu - Page 323 www.tuhoc.edu.vn (sin x cos x) sin x nên: cos x d(sin x cos x) sin x cos x T1 ln|sinx + cosx| C (b) Vì cos2x = cos2x – sin2x nên T2 T2 (cos x sin x)dx sin x cos x C (a) T1 (x sin x) C tan3 x tan2 xdx T2 tan3 x tan3 xd(tan x) tan x T2 cos2 x dx tan x tan2 xdx tan2 x ln cos x C (a) T1 = [ cos x (b) T2 1 sin 6x (c) T3 sin2x (d) T4 sin 8x 8 (e) T5 x (f) T6 cos 4x x 4 cos2x ] C C C sin6x sin 2x 2cos3 x sin 3x cos 8x sin 4x 16 sin2x sin x cos2 x sin x sin 4x sin 6x 12 cos x C C C htttp://tuhoc.edu.vn/blog HDedu - Page 324 HDedu - Page 325 ... 22 HDedu - Page 23 HDedu - Page 24 HDedu - Page 25 HDedu - Page 26 HDedu - Page 27 HDedu - Page 28 HDedu - Page 29 HDedu - Page 30 HDedu - Page 31 HDedu - Page 32 HDedu - Page 33 HDedu - Page... - Page 12 HDedu - Page 13 HDedu - Page 14 HDedu - Page 15 HDedu - Page 16 HDedu - Page 17 HDedu - Page 18 HDedu - Page 19 HDedu - Page 20 HDedu - Page 21 HDedu - Page 22 HDedu - Page 23 HDedu... 36 HDedu - Page 37 HDedu - Page 38 HDedu - Page 39 HDedu - 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