Inverse trig functions

Question 1

derivative of arcsine (u)

Answer 1

u’/(a-u^2)^1/2

Question 2

derivative of arccosine (u)

Answer 2

-u’/(a-u^2)^1/2

Question 3

derivative of arctangent (u)

Answer 3

u’/(a+u^2)

Question 4

derivative of arccotangent (u)

Answer 4

-u’/(a+u^2)

Question 5

derivative of secant (u)

Answer 5

u’/|u|(u^2-a)^1/2

Question 6

derivative of cosecant (u)

Answer 6

-u’/|u|(u^2-a)^1/2

Question 7

what inverse trig functions are negative

Answer 7

the ones that start with “co”
cosine, cotangent, cosecant

Question 8

integral of csc^2(u)du

Answer 8

-cot(u)+c

Question 9

integral of sec^2(u)du

Answer 9

tan(u)+c

Question 10

integral of tan^2(u)du

Answer 10

-u+tan(u)+c

Question 11

integral of cot^2(u)du

Answer 11

-u-cot(u)+c

Question 12

cosecant goes to

Answer 12

cotangent

Question 13

secant goes to

Answer 13

tangent

Question 14

integral of du/(a^2-u^2)^1/2

Answer 14

arcsin(u/a) + c

Question 15

integral of du/(a^2+u^2)

Answer 15

(1/a)arctan(u/a) + c

Question 16

integral of du/u(u^2-a^2)^1/2

Answer 16

(1/a)arcsec(

Question 17

Integral of tan(u)du

Answer 17

-ln|secx|+c

Question 18

Integral of cotu du

Answer 18

ln|sinx|

Question 19

Integral of secx

Answer 19

ln|secx + tanx|

Question 20

Integral of cscx

Answer 20

-ln|cscx + cotx|

Question 21

Is the integral of tangent positive or negative

Answer 21

Negative

Question 22

Is the integral of cot positive or negative

Answer 22

Negative