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45 Terms
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1
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∫0dx =
C
2
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∫\[g(x) + h(x)\]dx =
G(x) + H(x) + C
3
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∫xⁿdx =
1/n+1 \* x^(n+1) + C
4
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∫e^xdx =
e^x + C
5
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∫sin(x)dx =
\-cos(x) + C
6
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∫sec²(x)dx =
tan(x) + C
7
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∫sec(x)tan(x)dx =
sec(x) + C
8
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∫⅟√(1-x²)dx =
arcsin(x) + C
9
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∫kdx =
kx + C
10
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∫kf(x)dx =
kF(x) + C
11
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∫1/x dx =
ln(abs(x)) + C
12
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∫a^x dx =
a^x / lna + C
13
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∫cos(x)dx =
sin(x) + C
14
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∫csc²(x)dx =
\-cot(x) + C
15
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∫csc(x)cot(x)dx =
\-csc(x) + C
16
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∫⅟(1+x²) dx =
arctan(x) + C
17
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∫tan(x)dx =
ln(abs(sec(x))) + C
18
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∫cot(x)dx =
ln(abs(sin(x))) + C
19
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∫sec(x)dx =
ln(abs(secx + tanx)) + C
20
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∫csc(x)dx =
ln(abs(cscx - cotx)) + C
21
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∫ln(x)dx =
xlnx - x + C
22
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substitution for √a²-x²
x = a\*sin(theta)
23
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substitution for √a²+x²
x = a\*tan(theta)
24
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substitution for √x²-a²
x = a\*sec(theta)
25
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1-sin²x =
cos^2 (x)
26
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1 + tan²x =
sec^2 (x)
27
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sec²x - 1 =
tan^2 (x)
28
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√a²+x² becomes
a\*sec(theta)
29
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√x²-a² becomes
a\*tan(theta)
30
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√a²-x² becomes
a\*cos(theta)
31
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Integration by parts
integral(udv) = u\*v - integral(v\*du)
32
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LIATE
Logarithm, Inverse trig, Algebraic, Trigonometric, Exponential
33
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sin(2x) =
2sin(x)cos(x)
34
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sin²x (power reduction) =
(1 - cos(2x))/2
35
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cos²x (power reduction) =
(1 + cos(2x))/2
36
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sinAcosB =
1/2(sin(A+B) + sin(A-B))
37
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sinAsinB =
1/2(cos(A-B) - cos(A+B))
38
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cosAcosB = \`
1/2(cos(A-B) + cos(A+B))
39
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∫⅟(a²+x²) dx =
1/a \* arctan(x/a) + C
40
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average value of f on \[a, b\]
1/(b-a) \* integral from a to b of \[f(x)dx\]
41
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Arc length L of f(x) on \[a, b\]
L = ∫\[sqrt(1 + (dy/dx)^2) dx\] on \[a,b\]
42
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Surface area in terms of x across the x-axis
SA = ∫\[2πf(x) \* sqrt(1 + (dy/dx)^2) dx\] on \[a,b\]
43
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Surface area in terms of x across the y-axis
SA = integral from a to b of \[2 pi x \* sqrt(1 + (dy/dx)^2) dx\]
44
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Surface area in terms of y across the x-axis
SA = integral from a to b of \[2 pi y \* sqrt(1 + (dx/dy)^2) dy\]
45
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Surface area in terms of y across the y-axis
SA = integral from a to b of \[2 pi g(y) \* sqrt(1 + (dx/dy)^2) dy\]
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