Integrals Flashcards
To memorize basic integrals
1
Q
∫a dx
A
ax + C
2
Q
∫x dx
A
x^2/2 + C
3
Q
∫x^2 dx
A
x^3/3 + C
4
Q
∫(1/x) dx
A
ln|x| + C
5
Q
∫ex dx
A
e^x + C
6
Q
∫a^x dx
A
a^x/ln(a) + C
7
Q
∫ln(x) dx
A
x ln(x) − x + C
8
Q
∫cos(x) dx
A
sin(x) + C
9
Q
∫sin(x) dx
A
-cos(x) + C
10
Q
∫tan a(x) dx
A
-1/a ln(cos ax) + C = 1/a ln(sec ax) +C
11
Q
∫e^ax dx
A
1/a * a^ax
12
Q
∫sin^2 x dx
A
x/2 - 1/4 * sin2x
13
Q
∫cos^2 x dx
A
x/2 + 1/4 * sin2x
14
Q
∫sinx cosx dx
A
-1/2 cos^2 x
15
Q
∫tanx dx
A
-ln(cosx)
16
Q
∫tan^2 x dx
A
-x + tanx
17
Q
∫x^n dx
A
x^(n+1) / (n+1)
18
Q
∫u dv
A
uv -∫v du
19
Q
∫1/(ax + b) dx
A
1/a * ln(ax + b)
20
Q
∫lnx dx
A
xlnx - x
21
Q
∫1/x^2 dx
A
-1/x + C
