basic derivatives/integrals Flashcards
1
Q
tan(x) + C
A
sec^2(x)
2
Q
cot(x) + C
A
-csc^2(x)
3
Q
sec(x) + C
A
sec(x)tan(x)
4
Q
csc(x) + C
A
-csc(x)cot(x)
5
Q
e^x + C
A
e^x
6
Q
b^x + C
A
b^x ln(b)
7
Q
ln|x| + C
A
1/x
8
Q
log_b|x| + C
A
1/(x ln(b))
9
Q
arcsin(x) + C
A
(1-x^2)^(-0.5)
10
Q
arcos(x) + C
A
-(1-x^2)^(-0.5)
11
Q
arctan(x) + C
A
1/(1+x^2)
12
Q
arccot(x) + C
A
-1/(1+x^2)
13
Q
arcsec(x) + C
A
1/(|x| sqrt(x^2 - 1))
14
Q
arccsc(x) + C
A
-1/(|x| sqrt(x^2 - 1))
15
Q
ln|x + sqrt(x^2 + a^2)| + C
A
(x^2 + a^2)^(-0.5)
16
Q
5ln(|x-2|) - 4ln(|x+3|) + C
A
(x+23)/(x^2 + x - 6)
17
Q
sec^2(x)
A
tan(x) + C
18
Q
-csc^2(x)
A
cot(x) + C
19
Q
sec(x)tan(x)
A
sec(x) + C
20
Q
-csc(x)cot(x)
A
csc(x) + C
21
Q
e^x
A
e^x + C
22
Q
b^x ln(b)
A
b^x + C
23
Q
1/x
A
ln|x| + C
24
Q
1/(x ln(b))
A
log_b|x| + C
25
(1-x^2)^(-0.5)
arcsin(x) + C
26
-(1-x^2)^(-0.5)
arcos(x) + C
27
1/(1+x^2)
arctan(x) + C
28
-1/(1+x^2)
arccot(x) + C
29
1/(|x| sqrt(x^2 - 1))
arcsec(x) + C
30
-1/(|x| sqrt(x^2 - 1))
arccsc(x) + C
31
(x^2 + a^2)^(-0.5)
ln|x + sqrt(x^2 + a^2)| + C
32
(x+23)/(x^2 + x - 6)
5|x-2| - 4|x+3| + C
