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 =
n
1) 2) +C
n +1
1 1 1
3) ∫x 2
dx = −
x
+C 4) ∫ x dx = ln x + C
1 1 1 1
5) ∫ (ax + b) n
dx = −
a (n − 1)(ax + b) n −1
+C; 6) ∫ (ax + b) dx = a ln ax + b + C
7) ∫ sin x.dx = − cos x + C 8) ∫ cos x.dx = sin x + C
1 1
9) ∫ sin(ax + b)dx = − a cos(ax + b) + C 10) ∫ cos(ax + b)dx = a sin(ax + b) + C
1 1
11) ∫ 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 1
13) ∫ cos (ax + b) dx = a tan(ax + b) + C
2
14) ∫ sin 2
(ax + b)
dx = − cot(ax + b) + C
a
∫e ∫e
x
15) 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 ) n
17) e +C 18) . + C (n ≠ 1)
a a n +1
ax 1
∫ a dx = ∫x
x
19) +C 20) dx = arctgx + C
ln a 2
+1
1 1 x −1 1 1 x
21) ∫x 2
−1
dx = ln
2 x +1
+C 22) ∫x 2
+a 2
dx = arctg + C
a a
1 1 x−a 1
23) ∫x 2
−a 2
dx = ln
2a x + a
+C 24) ∫ 1− x2
dx = arcsin x + C
1 x 1
25) ∫ a −x 2 2
dx = arcsin
a
+C 26) ∫ x ±1 2
dx = ln x + x 2 ± 1 + C
1 x a2 x
27) ∫ 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 a2
29) ∫ 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-