Cong thuc-tich-phan

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Cong thuc-tich-phan

  1. 1. Ôn t p h th ng các công th c tính nguyên hàm Ôn thi TN-THPT CÔNG TH C TÍNH TÍCH PHÂN x n+1 ∫ k.dx = k.x + C ∫ x dx = n1) 2) +C n +1 1 1 13) ∫x 2 dx = − x +C 4) ∫ x dx = ln x + C 1 1 1 15) ∫ (ax + b) n dx = − a (n − 1)(ax + b) n −1 +C; 6) ∫ (ax + b) dx = a ln ax + b + C7) ∫ sin x.dx = − cos x + C 8) ∫ cos x.dx = sin x + C 1 19) ∫ sin(ax + b)dx = − a cos(ax + b) + C 10) ∫ cos(ax + b)dx = a sin(ax + b) + C 1 111) ∫ cos 2 x dx = ∫ (1 + tan 2 x).dx = tan x + C 12) ∫ sin 2 x dx = ∫ (1 + cot 2 x ) dx = − cot x + C 1 1 1 113) ∫ cos (ax + b) dx = a tan(ax + b) + C 2 14) ∫ sin 2 (ax + b) dx = − cot(ax + b) + C a ∫e ∫e x15) dx = e x + C 16) −x dx = −e − x + C 1 ( ax +b ) 1 (ax + b) n +1 ∫ e dx = ∫ (ax + b) .dx = ( ax + b ) n17) e +C 18) . + C (n ≠ 1) a a n +1 ax 1 ∫ a dx = ∫x x19) +C 20) dx = arctgx + C ln a 2 +1 1 1 x −1 1 1 x21) ∫x 2 −1 dx = ln 2 x +1 +C 22) ∫x 2 +a 2 dx = arctg + C a a 1 1 x−a 123) ∫x 2 −a 2 dx = ln 2a x + a +C 24) ∫ 1− x2 dx = arcsin x + C 1 x 125) ∫ a −x 2 2 dx = arcsin a +C 26) ∫ x ±1 2 dx = ln x + x 2 ± 1 + C 1 x a2 x27) ∫ x2 ± a2 dx = ln x + x 2 ± a 2 + C 28) ∫ a 2 − x 2 dx = 2 a2 − x2 + 2 arcsin + C a x 2 a229) ∫ x 2 ± a 2 dx = 2 x ± a2 ± 2 ln x + x 2 ± a 2 + C Biên so n: Nguy n Phan Anh Hùng -1-

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