basic forms of antiderivatives

Question 1

x^n

Answer 1

x^(n+1)/n+1+C

Question 2

e^kx

Answer 2

(e^kx)/k+C

Question 3

cos(x)

Answer 3

sin(x)+C

Question 4

sin(x)

Answer 4

-cos(x)+C

Question 5

sin(kx)

Answer 5

-cos(kx)/k+C

Question 6

cos(kx)

Answer 6

sin(kx)/k+C

Question 7

sec^2(x)

Answer 7

tan(x)+C

Question 8

sec(x)tan(x)

Answer 8

sec(x)+C

Question 9

tan(x)

Answer 9

ln|sec(x)|+C

Question 10

1/x^2+1

Answer 10

arctan(x)+C

Question 11

1/x^2+k^2

Answer 11

arctan(x/k)/k+C

Question 12

1/ sqrt(1-x^2)

Answer 12

arcsin(x)+C

Question 13

1/ sqrt(k^2-x^2)

Answer 13

arcsin(x/k)+C

Question 14

1/kx+b

Answer 14

ln|kx+b|/k+C

Question 15

k^x

Answer 15

k^x/ln(k)+C

Question 16

sec(x)

Answer 16

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

Question 17

1/sqrt(x^2-1)

Answer 17

arccosh(x)+C

Question 18

1/sqrt(x^2+1)

Answer 18

arcsinh(x)+C

Question 19

1/1-x^2

Answer 19

arctanh(x)+C