Integration Flashcards
1
Q
Integration by parts
A
∫ u dv = uv – ∫ v du
2
Q
∫ lnx dx
A
xlnx – x + C
3
Q
∫ sinx dx
A
–cosx + C
4
Q
∫ cosx dx
A
sinx + C
5
Q
∫ tanx dx
A
–ln |cosx| + C
6
Q
∫ cotx dx
A
ln |sinx| + C
7
Q
∫ secx dx
A
ln |secx + tanx| + C
8
Q
∫ cscx dx
A
–ln |cscx + cotx| + C
9
Q
∫ sin-1x dx
A
x sin-1x + √(1 – x2) + C
10
Q
∫ cos-1x dx
A
x cos-1x – √(1 – x2) + C
11
Q
∫ tan-1x dx
A
x tan-1x – 1/2 ln |x2 + 1| + C
12
Q
∫ cot-1x dx
A
x cot-1x + 1/2 ln |x2 + 1| + C
13
Q
∫ sec-1x dx
A
x sec-1x – sgnx ln |x + √(x2 – 1)| + C
14
Q
∫ csc-1x dx
A
x csc-1x + sgnx ln |x + √(x2 – 1)| + C
15
Q
∫a∞ ƒ(x) dx
A
limb→∞ ∫ab ƒ(x) dx
16
Q
∫-∞b ƒ(x) dx
A
lima→-∞ ∫ab ƒ(x) dx
17
Q
∫ab ƒ(x) dx =
If ƒ is discontinuous at x = c in [a, b]
A
limk→c+ ∫kb ƒ(x) dx + limk→c– ∫ak ƒ(x) dx
18
Q
∫ du / √ ( 1 – u2 )
A
sin-1(u) + C
for u2 < 1
19
Q
∫ du / ( 1 + u2 )
A
tan-1(u) + C
20
Q
∫ du / ( u √( u2 – 1) )
A
sec-1(u) + C
for u2 > 1
21
Q
∫ax dx
A
1 / lna ax + C
