antiderivatives rules flashcards

Question 1

What is ∫ xⁿ dx?

Answer 1

(x^(n+1)) / (n+1) + C (for n ≠ -1)

C is the constant of integration

Question 2

What is ∫ cos x dx?

Answer 2

sin x + C

C is the constant of integration

Question 3

What is ∫ sin x dx?

Answer 3

-cos x + C

C is the constant of integration

Question 4

What is ∫ sec² x dx?

Answer 4

tan x + C

C is the constant of integration

Question 5

What is ∫ csc x cot x dx?

Answer 5

-csc x + C

C is the constant of integration

Question 6

What is ∫ sec x tan x dx?

Answer 6

sec x + C

C is the constant of integration

Question 7

What is ∫ csc² x dx?

Answer 7

-cot x + C

C is the constant of integration

Question 8

What is ∫ e^x dx?

Answer 8

e^x + C

C is the constant of integration

Question 9

What is ∫ a^x dx?

Answer 9

(a^x) / ln(a) + C (for a > 0, a ≠ 1)

C is the constant of integration

Question 10

What is ∫ (1/x) dx?

Answer 10

ln |x| + C

C is the constant of integration

Question 11

What is ∫ (1 / (a² + u²)) du?

Answer 11

(1/a) tan⁻¹(u/a) + C

C is the constant of integration

Question 12

What is ∫ (1 / √(a² - u²)) du?

Answer 12

sin⁻¹(u/a) + C

C is the constant of integration

Question 13

What is ∫ 0 dx?

Answer 13

c

Question 14

What is ∫ k dx?

Answer 14

kx+c

Question 15

What is ∫ k f(x) dx?

Answer 15

k ∫ f(x) dx