Integration formulas

Question 1

∫ x^n dx

Answer 1

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

Question 2

∫ 1/x dx

Answer 2

ln|x| +C

Question 3

∫e^x dx

Answer 3

e^x + C

Question 4

∫b^x dx

Answer 4

b^x/ln|b| +C

Question 5

∫sin x dx

Answer 5

-cos x + C

Question 6

∫cos x dx

Answer 6

sin x + C

Question 7

∫sec^2 x dx

Answer 7

tan x + C

Question 8

∫ csc^2 x dx

Answer 8

• cot x + C

Question 9

∫(sec x)(tan x) dx

Answer 9

sec x +C

Question 10

∫(csc x)(cot x)dx

Answer 10

-csc x +C

Question 11

∫sec x dx

Answer 11

ln|sec x + tan x| + C

Question 12

∫ csc x dx

Answer 12

ln|csc x - cot x| + C

Question 13

∫ tan x dx

Answer 13

ln|sec x| +C

Question 14

∫cot x dx

Answer 14

ln|sin x| + C

Question 15

∫ sinh x dx

Answer 15

cosh x + C

Question 16

∫ cosh x dx

Answer 16

sinh x + C

Question 17

∫ dx/(x^2 + a^2)

Answer 17

1/a*tan^(-1)(x/a) + C

Question 18

∫ dx/sqrt(a^2 - x^2)

Answer 18

sin^(-1)( x/a) + C (a>0)

Question 19

∫ dx/(x^2 - a^2)

Answer 19

1/2a*ln|(x-a)/(x+a)|

Question 20

∫ dx/sqrt(x^2 +- a^2)

Answer 20

ln| x + sqrt(x^2 +- a^2)|