... ∫ 2 2 π − cos ( π − t) − cos t − cos t − cos t π π π d(cos t) d(cos t) d(cos t) = −π ∫ − I ⇔ 2I = −π ∫ = π∫ 2 − cos t − cos t cos t − π π d(cos t) π cos t − ⇔I= ∫ = ln cos2 t − 4 cos t + Câu15:: ... đó: dx = costdt Lại có: x2 dx − x2 = sin t.cos tdt − sin t = x= ⇒ t = π Đổi cận: với x= ⇒t= sin t.cos tdt sin t cos tdt = = (1 − cos2t)dt cos t cos t π/ π/ 1 I = ∫ (1 − cos2t)dt = ... 4 4 π π π / cos ( − t) + sin ( − t) cos t + sin t cos x + sin x 2 Do đó: 2I = π/ ∫ π/2 cos4 x + sin x π π dx = ∫ dx = ⇒ I = 4 cos x + sin x Câu11:: Tính tích phân: I = 1/ 1− x cos x.ln ÷dx...
... π π sin x sin x + cos x ) ' π dx = 1 − ( ∫ sin x + cos x ÷dx = sin x + cos x 20 π π sin x − cos x 14 26 dx = − ∫ d cos x = + ÷ = − cos x cos x 27 3cos x cos x π π 6 π ∫ 16, ... cos x − + ÷ = − 0 15 π ∫ ( − cos x + cos x ) d cos x π π 4sin x 22, I 22 = ∫ dx = + cos x π 23, I 23 = ∫ ln 24, I 24 = 4sin x ∫ + cos x d ( cos x ) ∫ 25, I 25 = ∫ sin x cos3 x dx = − + cos ... 2+t 0 ( 2+t) ( 2+t) π t π cos x ∫ ( sin x + cos x + ) 20, I 20 = dx = ∫ ( sin x + cos x ) ( cos x − sin x ) dx ( sin x + cos x + ) Đặt t = sin x + cos x + ⇒ dt = cos x − sin x , x = → t = 3;...
... ∫ 2 2 π − cos ( π − t) − cos t − cos t − cos t π π π d(cos t) d(cos t) d(cos t) = −π ∫ − I ⇔ 2I = −π ∫ = π∫ 2 − cos t − cos t cos t − π π d(cos t) π cos t − ⇔I= ∫ = ln cos2 t − 4 cos t + Câu15:: ... ( x.cos x ) ( cos x − 3xcos xsin x ) dx = ∫ ( 3 π x3cos9x π3 x.cos x d x.cos x = = 3 12288.3 ) ( ) Giải: π Câu 151: I= ∫ π ( x.cos x ) ( cos x − 3xcos x sin x )dx = ∫ ( 3 π x cos6 x π2 x.cos ... ( x.cosx ) π ( cosx − xsin x ) dx = ∫ ( x.cosx ) d ( x.cosx ) = π x3cos3x π3 = 3 5184 Giải: π x cosx − xsin x dx ÷ cosx ÷ Câu 94:I= ∫ cos x π x d x = cosx ÷ cosx...
... x 0 ∫ tan π sin x s inx − cos x s inx s inx s inx = = − cos x cosx cos x cosx cos3 x cosx ( − cos x ) x= cos x − cos x + cos x = = ( + tan x ) − +1 cos x cos x cos x π π +2 ⇒ I = ∫ ( + ... J = ∫ cosx+1 dx = ∫ x 2 0 cos 0 π f sin x cos x dx + cosx ∫ • • sin x cos x 2sin x cos x cos x − 2 = = + s inx= ( cosx-1) + + cosx s inx + cosx + cosx + cosx + cosx π ... π e cos3 x ∫ + cosx dx • • cos3 x cos3 x + 1 1 + cos2x dx= − = cos x − cosx+1= − cosx+11 + cosx + cosx + cosx 1+cosx 1+cosx π π π π 12 1 x 3π ⇒ I = ∫ ( + cos2x+2cosx ) dx- ∫ dx = 3x + sin...
... I+J = ∫ cos2007 t dx = J (1) sin2007 t + cos2007 t ∫ sin2 x dx J = sin x + cos x ∫ π cos n x π dx = , n ∈ Z+ n n sin x + cos x π ∫ cos2 x dx sin x + cos x Gi i cos x π dx = ∫ (sin x − ( cos x)dx ... sin cosin ch n) Tính tíchphân I = ∫ cos x sin2 xdx π I= ∫ cos Gi i π x sin2 xdx = π π 1 ∫ cos2 x sin2 2xdx = 16 ∫ (1 − cos 4x)dx + ∫ cos 2x sin2 2xdx 0 π π π 2 x 1 sin 2x = π = (1 − cos ... i hàm cos Phương pháp chung: t t = sinx ó dt = cosx.dx, sau ó ưa tíchphân ban Chú ý: cos2 x = sin2 x = − t2 lê u v tíchphân theo bi n t văn (cos x)2n+1 = (cos2 x)n cosx = (1 − t2 )n cosx π...
... cos3 x dx sin x cos x + sin x cos x dx + sin x sin x dx sin x + cos6 x π /2 sin x ∫ + cos x dx đs: 3 ( 16 − 1) đs − đs: dx 70 π − /4 cos x.cos x + 4÷ π /2 sin x dx 71 S = ∫ sin x + cos ... = ∫ 77 U = π dx − cos x ∫ 75 S = π + ln đs: e −1 π /2 ln đs: x ln 73 Q = đs: dx 19 đs: − 10 đs: + ln ln đs: O= 72 P = đs 25ln − 16 ln + e 61 E = ∫ cos x.dx ∫ 13 − 10sin x − cos x 2ln đs: 11 + ... x 55 Y = ∫ 58 C = dx cos x ln ( ex ) e đs : đs : π /2 ∫ 4π + 3ln cos x.cos 2 x dx ; J = a) Tính I + J I – J π + −2 π /2 ∫ sin x.cos 2 x dx http://violet.vn/toan_cap3 b) Tính I , J đs: π/4 ; ;...
... x + 3cos x − cos x − cos x.cos2 x + cos x + 3cos x.cos2 x dx 16 = sin x 3sin x + (1 + cos12 x + ( cos8 x + cos4 x ) ) − 16 16 ∫ ( ) + cos18 x + 3cos x + cos12 x +3 cos2 x dx ∫ ... 4, ( cot x )6 dx = D4 = ∫ ∫ sin x cos2 xdx ( cos2x )5 5, E1 = ∫ ( sin x ) ( cos2x )3 dx = ∫ = 1 ∫ sin x d ( sin2x ) = −10sin5 x + C 2 − cos6 x cos6 x + 3cos x dx = ∫ cos6 x + 3cos ... www.VNMATH.com 6, E2 = ∫ ( sin x ) ( cos5x ) dx = ∫ ( sin x ) ( sin x ) ( cos5x )2 dx 3sin x − sin x − cos2 x + cos10 x dx 2 cos12 x + cos8 x = ∫ ( 3sin x − sin x ) 1 + cos10 x − cos2 x −...
... − + ( π 29) I = ∫ π ) cos x ( 2cot x + 3cot x + 1) sin x e + cot x sin x dx π =∫ π cot x ( 2cot x + 3cot x + 1) sin x e cot x + cot x +1 dx u +u +1 du; t = u + u + u = cot x ⇒ du = − dx ⇒ I ... π dx 10) I = ∫ π cos x.cos x + ÷ 4 1 π Ta có: cosx cos (x + ) = cosx ( cosx sinx) = cos2x (1- tanx) 2 => I = π π π 3− d ( tan x ) dx = − 2∫ = − ln tan x − 06 = − ln cos x ( − tan x ) tan ... hoctoancapba.com π Tính: I = 2sìn2x.cos xdx = − cos xd ( cos x ) = − cos5 x = ∫ ∫ 5 hoctoancapba.com GV: PHẠM NĂNG KHÁNH Vậy I = I1 − I = π 6) I = ∫π − 2− ÷− ln ln sin x − cos x dx cos x π...
... dx 12 sin x cos x dx 13 sin x + sin x cos x cos x 14 cos x dx + cos x 15 cos x dx cos x 17 cos x dx + cos x cos xdx 19 (1 cos x) 0 sin x cos x + 20 sin x + cos x + dx xdx ... + dx sin x cos xdx (sin x + cos )dx cos x(sin x + cos x)dx (2 sin x sin x cos x cos x)dx sin x dx (sin 10 x + cos10 x cos x sin x)dx dx cos x 11 sin x dx + cos x 10 dx ... 17 e cosxdx x e 18 20 e +2 19 sin xdx sin x 21 e cosxdx 22 x e cosx cosx sin xdx xcos xdx sin xdx +2 23 sin xdx xcos xdx 24 sin 25 sin x dx + 3cosx xcos xdx 27 cot gxdx...
... dx i/ l/ ∫e dx m/ ∫ x.e dx x ∫ ( + x ) e dx ∫ ( + x ) cos xdx π ∫ cos x.e n/ e/ ∫ ( x + 1) e dx x f/ π ∫ ( + x ) sin xdx e ∫ x ln xdx dx ∫ x.cos xdx c/ h/ sin x π x ∫ x − dx k/ 0 g/ ∫ x.sin xdx...
... ( cos x + sin x ) = sin10 x + cos10 x − cos6 x sin x − cos4 x sin x = − sin x ( cos4 x − sin x ) + cos6 x ( cos4 x − sin x ) = ( cos4 x − sin x ) ( cos6 x − sin x ) = ( cos2 x − sin x ) ( cos2 ... + sin x ) ( cos2 x − sin x ) ( cos4 x + cos2 x sin x + sin x ) = cos2 2x ( − cos2 x sin x ) cos2 2x.sin 2x + cos 4x sin 4x 1 − cos8x = cos2 2x − sin 2x ÷ = cos2 2x − = − = + cos 4x − 16 ... Tính tíchphân : I = cos5 x cos 7xdx ∫ π π π 0 I = ∫ cos5 x cos ( 6x + x ) dx = ∫ cos 6x cos5 x cos xdx − ∫ sin 6x cos x sin xdx = J − K π π du = −6sin x cos5 xdx 2 u = cos x 1 Tính J...
... − ∫ − cos2 (π − t) − cos2 t − cos2 t ∫ − cos2 t π 0 π π π d(cos t) d(cos t) d(cos t) − I ⇔ 2I = −π ∫ = π∫ 2 − cos t − cos t cos t − = −π ∫ π π d(cos t) π cos t − ⇔I= ∫ = ln cos2 t − 4 cos t ... ∫ x 5cosx ( 3cosx − xsinx ) dx Giải: π x3cosx I=∫ π x 3cosxd ( 3x cosx − x sinx )dx=∫ Câu 46: Tính : I= π sinx ∫0 e sin2x + ( x cosx ) π =0 ( x cosx )dx= 2 3 sinx − cosx dx sinx + cosx ... t = Đặt x = sint, đó: dx = costdt Lại có: x2 dx − x2 = sin t.cos tdt sin t.cos tdt sin t cos tdt = = = (1 − cos2t)dt cos t cos t − sin2 t π/ Khi đó: I = ∫ (1 − cos2t)dt = Câu5: Tính tích phân...
... −5 hoctoancapba.com BàitậpTíchphân Trần Sĩ Tùng Dạng 2: Tíchphânphần Câu 31 I = π ∫e s inx sin xdx π u = sin x du = cos xdx ⇒ • I = es inx sin x cos xdx Đặt sin x cos xdx v = esin ... + 2e + = − 2 + 2e 3 x + ln x ln x • I =∫ e ln x + ln x Câu 19 I = ∫ dx x Trang 28 hoctoancapba.com BàitậpTíchphân • Đặt t = + ln2 x ⇒ dt = Câu 20 I = e2 •I= e ∫ e e dx d (ln x ) =∫ = x ln ... hoctoancapba.com BàitậpTíchphân Câu I= ln Trần Sĩ Tùng x e − dx ∫ • Đặt 1 dt ⇒ I = 3∫ − ÷dt = − 3∫ ...
... − = cos t (1 + cos t ) 2sin t − (2 cos t)2 − x − x dx dt = 2π ∫ ( + cos t + cos2t ) dt = π π π 3 + −4 2 • Đặt x = sin t ⇒ I = (cos t − sin t ) cos tdt = π + − ∫ 12 8 Trang hoctoancapba.com Trần ... I = ∫ π 12 − x2 2x4 dx Đặt x = 2sin t ⇒ dx = cos tdt π 12 π 12 6 cos tdt = ∫ cot t ÷dt = − ∫ cot t.d (cot t ) = ⇒ I2 = ∫ 8π 8π sin t π sin t Vậy: I = ( − ) 16 x dx − x6 Câu 31 I = ... hoctoancapba.com ) Trần Sĩ Tùng − x dx 2x4 • Ta có: I = ∫ 2x 4 − x2 dx − ∫ 2x4 dx −4 + Tính I1 = ∫ dx = ∫ x dx = 21 16 2x + Tính I = ∫ π 12 − x2 2x4 dx Đặt x = 2sin t ⇒ dx = cos tdt π 12 π 12 6 cos...
... 12 ∫ cos xdx = π 2 ∫ cos x.dx = Vậy I = Câu 2 ∫ ( − sin x ) d (sin x ) = 15 π (1 + cos2 x ).dx = ∫ 20 π – 15 π I = ∫ cos x cos xdx π • I = cos2 x cos2 xdx = ∫ π 12 π 12 ∫ (1 + cos x ) cos xdx ... =− sin x cos x sin x ∫ − π cos2 x π π • I= sin x − cos2 x π cos x Câu 28 I = π π − cos2 x dx = ∫ − π dx + ∫ ∫ sin x + dx sin x cos x cos x dx = π sin x cos x sin x dx = ∫ − π sin x cos x sin ... 4 + cos t d (cos t ) dt = −π ∫ cos4 x sin x ∫ cos3 x + sin3 x dx • Đặt x = sin t cos t π dt = − t ⇒ dx = −dt ⇒ I = − ∫ cos3 t + sin3 t π π sin x cos x ∫ cos3 x + sin3 x dx ⇒ 2I = π ∫ 4 cos x...