NGƠ NHẬT MINH
CÔNG THỨC TÍCH PHÂN
+
= + C n
x dx x
n n
1
1
3) ∫ =− +C
x
dx
x
1 1
1
+
−
−
=
b ax n
a
dx b
1 )
(
1
+b dx a ax b C
1 )
( 1
7) ∫sinx.dx= − cosx+C 8) ∫cosx.dx= sinx+C
a dx b
a dx b
11) ∫ dx=∫ +tg x dx=tgx+C
x (1 ).
cos
sin
2
+b dx a tg ax b C
1 )
(
cos
1
+b dx a g ax b C
1 )
( sin
1
2
15) ∫e x dx =e x +C
16) ∫e−x dx = −e−x +C
17) ∫ + = e + +C
a dx
e(ax b) 1 (ax b)
+
+
=
n
b ax a dx b
1
) (
1 )
a
a dx
a
x x
+ dx arctgx C
x 1
1
2
+
−
=
x dx
1 ln 2
1 1
1
x arctg a
dx a x
1 1
2 2
+
−
=
a x a
dx a
1 1
2
−x dx arcsinx C
1
1
x dx
x
1
2
2
±a dx x x a C
x
2 2 2
a
x a
x a
x dx x
2 2
2 2 2 2
2
29) ∫ x2 ±a2dx= x x2 ±a2 ±a2 lnx+ x2 ±a2 +C
2 2