Antiderivative/Integral Formulas

Question 1

∫ dx

Answer 1

x + C

Question 2

∫ x^n dx

Answer 2

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

Question 3

∫ dx/x

Answer 3

ln|x| + C

Question 4

∫ e^x dx

Answer 4

e^x + C

Question 5

∫a^x dx

Answer 5

[1/ ln(a)] • a^x + C

Question 6

∫ ln(x) dx

Answer 6

x • ln(x) - x + C

Question 7

∫ sin(x) dx

Answer 7

• cos(x) + C

Question 8

∫ cos(x) dx

Answer 8

sin(x) + C

Question 9

∫ tan(x) dx

Answer 9

• ln|cos(x)| + C

Question 10

∫ sec(x) dx

Answer 10

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

Question 11

∫ csc(x) dx

Answer 11

• ln|csc(x) + cot(x)| + C

Question 12

∫ cot(x) dx

Answer 12

ln|sin(x)| + C

Question 13

∫ sec²(x) dx

Answer 13

tan(x) + C

Question 14

∫ csc²(x) dx

Answer 14

• cot(x) + C

Question 15

∫ sec(x) • tan(x) dx

Answer 15

sec(x) + C

Question 16

∫ csc(x) • cot(x) dx

Answer 16

• csc(x) + C

Question 17

∫ dx / √(a² - x²)

Answer 17

sin-¹(x/a) + C

Question 18

∫ dx / x√(a² - x²)

Answer 18

(1/a) • sec-¹(|x|/a) + C

Question 19

∫ dx / (a² + x²)

Answer 19

(1/a) • tan-¹(x/a) + C