Pure - Integration

Question 1

What is the integral of “xⁿ” with respect to x?

Answer 1

(xⁿ⁺¹)/(n+1) + c

Question 2

What is the integral of “e⁽ᵃˣ⁺ᵇ⁾” with respect to x?

Answer 2

e⁽ᵃˣ⁺ᵇ⁾/a + c

Question 3

What is the integral of “af’(x)/f(x)” with respect to x?

Answer 3

aLn|f(x)| + c

Question 4

What is the integral of “sec²(x)” with respect to x?

Answer 4

tan(x) + c

Question 5

What is the integral of “cosec(x) cot(x)” with respect to x?

Answer 5

-cosec(x) + c

Question 6

What is the integral of “cosec²(x)” with respect to x?

Answer 6

-cot(x) + c

Question 7

What is the integral of “sec(x)tan(x)” with respect to x?

Answer 7

sec(x) + c

Question 8

What is the integral of “cot(x) cosec(x)” with respect to x?

Answer 8

-cosec(x) + c

Question 9

What is the integral of “cos(ax+b)” with respect to x?

Answer 9

1/a sin(ax+b) + c

Question 10

What is the integral of “sin(ax+b)” with respect to x?

Answer 10

-1/a cos(ax+b) + c

Question 11

What is the integral of “f’(ax+b)” with respect to x?

Answer 11

1/a f(ax+b) + c

Question 12

What is the integral of “(ax+b)ⁿ” with respect to x?

Answer 12

1/(n+1) 1/a (ax+b)ⁿ⁺¹ + c

Question 13

What is the integral of “tan(kx)” with respect to x?

Answer 13

1/k Ln|sec(kx)|

IN FORMULA BOOK

Question 14

What is the integral of “cot(kx)” with respect to x?

Answer 14

1/k Ln|sin(kx)|

IN FORMULA BOOK

Question 15

What is the integral of “cosec(kx)” with respect to x?

Answer 15

• -1/k Ln|cosec(kx) + cot(kx)|
• 1/k Ln|tan(0.5kx)|

IN FORMULA BOOK

Question 16

What is the integral of “sec(kx)” with respect to x?

Answer 16

• 1/k Ln|sec(kx) + tan(kx)|
• 1/k Ln|tan(0.5kx + π/4 )|

IN FORMULA BOOK