Known Antiderivative, Trig Identities, And Other Known Things

Question 1

int: 1/x

Answer 1

ln|x|

Question 2

int: -sin(x)

Answer 2

cos(x)

Question 3

int: sec^2(x)

Answer 3

tan(x)

Question 4

int: sec(x)tan(x)

Answer 4

sec(x)

Question 5

int: -csc^2(x)

Answer 5

cot(x)

Question 6

int: -csc(x)cot(x)

Answer 6

csc(x)

Question 7

int: 1/sqrt(1-x^2)

Answer 7

arcsin(x)

Question 8

int: 1/(1+x^2)

Answer 8

arctan(x)

Question 9

int: a^x

Answer 9

(1/ln(a)) (a^x)

Question 10

int: e^x

Answer 10

e^x

Question 11

int: af(x)

Answer 11

aF(x)

Question 12

int: f’(x)/f(x)

Answer 12

ln|f(x)|

Question 13

int: sec(x)

Answer 13

ln|sec(x) + tan(x)|

Question 14

int: csc(x)

Answer 14

-ln|csc(x) - tan(x)|

Question 15

cos^2(x) + sin^2(x)=

Answer 15

1

Question 16

1 + tan^2(x)=

Answer 16

sec^2(x)

Question 17

sin(2x) =

Answer 17

2sin(x)cos(x)

Question 18

cos(2x)=

Answer 18

cos^2(x) - sin^2(x)

Question 19

2cos^2(x) - 1=

Answer 19

cos(2x)

Question 20

1 - 2sin^2(x)=

Answer 20

cos(2x)

Question 21

2cos^2(x)=

Answer 21

1 + cos(2x)

Question 22

2sin^2(x)=

Answer 22

1-cos(2x)

Question 23

what is e^x in terms of a series

Answer 23

summation at n=0 to infinity: x^n/n!