Integrals

Question 1

What is the derivative of a constant?

Answer 1

d/dx (n) = 0

Question 2

What is the derivative of x?

Answer 2

d/dx (x) = 1

Question 3

What is the derivative of x^n?

Answer 3

d/dx (x^n) = n*x^(n-1)

Question 4

What is the derivative of e^x?

Answer 4

d/dx (e^x) = e^x

Question 5

What is the derivative of ln(x)?

Answer 5

d/dx (ln(x)) = 1/x

Question 6

What is the derivative of sin(x)?

Answer 6

d/dx (sin(x)) = cos(x)

Question 7

What is the derivative of cos(x)?

Answer 7

d/dx (cos(x)) = -sin(x)

Question 8

What is the derivative of tan(x)?

Answer 8

d/dx (tan(x)) = sec^2(x)

Question 9

What is the derivative of cot(x)?

Answer 9

d/dx (cot(x)) = -csc^2(x)

Question 10

What is the derivative of sec(x)?

Answer 10

d/dx (sec(x)) = sec(x)tan(x)

Question 11

What is the derivative of csc(x)?

Answer 11

d/dx (csc(x)) = -csc(x)cot(x)

Question 12

What is the derivative of arcsin(x)?

Answer 12

d/dx (arcsin(x)) = 1/sqrt(1-x^2)

Question 13

What is the derivative of arccos(x)?

Answer 13

d/dx (arccos(x)) = -1/sqrt(1-x^2)

Question 14

What is the derivative of arctan(x)?

Answer 14

d/dx (arctan(x)) = 1/(1+x^2)

Question 15

What is the derivative of arccot(x)?

Answer 15

d/dx (arccot(x)) = -1/(1+x^2)

Question 16

What is the derivative of arcsec(x)?

Answer 16

d/dx (arcsec(x)) = 1/(|x|*sqrt(x^2-1))

Question 17

What is the derivative of arccsc(x)?

Answer 17

d/dx (arccsc(x)) = -1/(|x|*sqrt(x^2-1))

Question 18

What is the integral of dx?

Answer 18

∫ dx = x + C

Question 19

What is the integral of 1?

Answer 19

∫ 1 dx = x + C

Question 20

What is the integral of x^n?

Answer 20

∫ x^n dx = (x^(n+1))/(n+1) + C

Question 21

What is the integral of e^x?

Answer 21

∫ e^x dx = e^x + C

Question 22

What is the integral of ln(x)?

Answer 22

∫ ln(x) dx = x*ln(x) - x + C

Question 23

What is the integral of cos(x)?

Answer 23

∫ cos(x) dx = sin(x) + C

Question 24

What is the integral of sin(x)?

Answer 24

∫ sin(x) dx = -cos(x) + C

Question 25

What is the integral of sec^2(x)?

Answer 25

∫ sec^2(x) dx = tan(x) + C

Question 26

What is the integral of csc^2(x)?

Answer 26

∫ csc^2(x) dx = -cot(x) + C

Question 27

What is the integral of tan(x)sec(x)?

Answer 27

∫ tan(x)sec(x) dx = sec(x) + C

Question 28

What is the integral of cot(x)csc(x)?

Answer 28

∫ cot(x)csc(x) dx = -csc(x) + C

Question 29

What is the integral of arcsin(x)?

Answer 29

∫ arcsin(x) dx = x*arcsin(x) + sqrt(1-x^2) + C

Question 30

What is the integral of arccos(x)?

Answer 30

∫ arccos(x) dx = x*arccos(x) - sqrt(1-x^2) + C

Question 31

What is the integral of 1/(1+x^2)?

Answer 31

∫ 1/(1+x^2) dx = arctan(x) + C

Question 32

What is the integral of 1/(1+x)?

Answer 32

∫ 1/(1+x) dx = arccot(x) + C

Question 33

What is the integral of 1/(x*sqrt(x^2-1))?

Answer 33

∫ 1/(x*sqrt(x^2-1)) dx = arcsec(x) + C

Question 34

What is the integral of 1/(x*sqrt(x^2-1))?

Answer 34

∫ 1/(x*sqrt(x^2-1)) dx = arccsc(x) + C