NGUYEN HAM HUU TY

<span class='text_page_counter'>(1)</span>BÀI TẬP NGUYÊN HÀM HỬU TỶ (Dùng phương pháp hệ số bất định đưa về tổng ) 1.. x2 −5 x +9 ∫ x2 −5 x +6 dx. 2. 2 x 2 +41 x − 9 ∫ x3 −2 x 2 −11 x +12 dx 3.. 6.. 5 x 2 +6 x+ 8 ∫ ( x −3 )2 ( x +1 )2 dx. 7.. ∫ x2 −5 x +6 dx. 4 x +11. 8.. ∫. 9.. dx ∫ x 4 − 4 x 2 +3. 1. ∫ x3 −2 x 2+ x dx. 4.. ( x 2+3 x +2 ). 2. dx. 3. 4. 3. 6x dx ∫ x+1. 10.. 2. − 6 x +12 x + 6 dx ∫ xx −6 x 2+ 12 x −8. ∫. 11.. 4. 5.. 1. +1 dx ∫ xx6 −1. x +1 x ( 1+ xe x ). dx. ĩ sin x +cos x dx 12. ∫ 3+sin 2 x. 13.. cot x. ∫ 1+ sin9 x dx. 14. 2. ∫ x 4 +2 x 3x−−x 21+ 2 x +1 dx 15.. ∫. dx x 4 ( 1+ x2 ). x2 dx 16. ∫ 2 ( 1− x 2) dx. 17.. ∫ x (x10 +1). 18.. +1 dx ∫ xx6 −1. 4. HD: 1.. (x 4+ x2 +1)− x2 x 4 +1 1 x2 = = − x 6 −1 (x 2 − 1)(x 4 + x2 +1) x 2 − 1 x 6 − 1. . 1 1 1 1 = − x −1 2 x − 1 x+1. . x2 x 6 −1. 2.. (. 2. đặt. t=x. ). 3. x 2 −5 x+ 9 1 1 =1+3 − 2 x−3 x−2 x −5 x+ 6. (. ). 2 x 2+ 41 x − 9 A B C = + + 3. 3 2 x −2 x −11 x +12 x −1 x +3 x −4 . 2 x 2 +41 x − 9= A ( x +3 )( x − 4 ) +B ( x −1 ) ( x − 4 ) +C ( x −1 ) ( x+ 3 ). Gán x=1,x= -3 ,x=4 tìm A ,B ,C 4.. 1 1 A B C = = + + 3 2 2 x x +1 x −2 x + x x ( x+ 1 ) ( x +1 )2. như bài 3 5.. x 4 − 6 x 3 +12 x2 +6 − 8 x +6 =x+ 3 2 x −6 x +12 x −8 ( x −2 )3.

<span class='text_page_counter'>(2)</span> . − 8 x+ 6 A B C = + + 2 MS x −2 ( x −2 ) ( x − 2 )3. tìm A,B,C. 2. 5 x + 6 x +8 A B C D = + + + 2 2 2 ( x −3 ) ( x+1 ) ( x − 3 ) ( x − 3 ) x+ 1 ( X +1 )2. 6. 7. 8. 9.. 4 x+ 11 A B = + x −3 x −2 x −5 x+ 6 2. 1. ( x2 +3 x+ 2 ). [. = 2. 2. 1 1 − x+1 x +2. ]. 1 1 1 1 1 = 2 = − 2 4 2 2 2 x − 4 x +3 ( x −1 ) ( x − 3 ) 2 x −3 x −1. 11.. [. e x ( x +1 ) x +1 = x ( 1+xe x ) e x x ( 1+ xe x ). 13.. cot xdx cos xdx 1 t8 = = − 1+sin 9 x sin x ( 1+ sin 9 x ) t 1+ t 9 x −1 dx= 4 3 x + 2 x − x 2+2 x +1. 1 1 − t −1 t. π √2 cos x − dx. (. (. 4). (. 2 1+ cos2 x −. π 4. π √ 2 cos x − dx =. )). (. [. (. với t=sĩn. 2. ( x + 1x ) +2( x+ 1x ) −3. 1 1 1 1 = 4 − 2+ 2 2 x ( 1+ x ) x x 1+ x. 16.. x2 1 1 dx= − 2 2 2 2 2 ( 1− x ) ( 1 − x ) 1− x. dx. t=x+. 4.   1 x ( x 10+1 ). =. 1 1 1 1 = − x −1 2 x −1 x +1. [. 2. 1 2 2. ( 1− x ). x9 x 10 ( x 10 +1 ). =. 4. ]. 1 1 1 2 + − 4 ( x −1 )2 ( x +1 )2 ( x − 1 ) ( x +1 ). [. đặt t=1+ x 10. ). 2 2− sin2 x −. 2. 15.. 17.. ⇒. (1 − x1 ). 2. 14.. ]. đặt t=1+xe x. ( sin x+ cos x ) dx sin x+ cos x = 12.. 3+ sin 2 x dx= 2 2+ ( sin x +cos x ). 3. 6x 6 =6 ( x 2 − x+1 ) − x +1 x +1. 10.. ]. 1 x. π 4. )]. (. đặt t=sin x −. π 4. ).

<span class='text_page_counter'>(3)</span> 4. 2. x +1 1 x = 2 − 6 18. 6 x −1 x −1 x −1 Nguyễn văn Phép Gv. PTTH BÌNH MINH.

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