Derivatives and Integrals of Trig functions

Question 1

d/dx sin(x)

Answer 1

cos(x)dx

Question 2

d/dx cos(x)

Answer 2

-sin(x)dx

Question 3

d/dx tan(x)

Answer 3

sec^2(x)dx

Question 4

d/dx sec(x)

Answer 4

sec(x)tan(x)dx

Question 5

d/dx csc(x)

Answer 5

-csc(x)cot(x)dx

Question 6

d/dx cot(x)

Answer 6

-csc^2(x)

Question 7

int cos(x)

Answer 7

sin(x) + c

Question 8

int sin(x)

Answer 8

-cos(x)

Question 9

int tan(x)

Answer 9

ln(sec(x)) + c

Question 10

int sec(x)

Answer 10

ln(sec(x) + tan(x)) + c

Question 11

int sec^3(x)

Answer 11

1/2sec(x)tan(x) + 1/2ln(sec(x) + tan(x)

Question 12

Integration by parts formula

Answer 12

uv = int(vdu)

Question 13

if a^2 - x^2

Answer 13

x = asin(u) dx = acos(u)dx

Question 14

x^2 - a^2

Answer 14

x = secudu dx = asec(u)tan(u)

Question 15

x^2 + a^2

Answer 15

x = tan(u) dx = sec^2(u)