Integration 2: Integration by substitution

Question 1

integral of (ax + b)^n

Answer 1

1/a x 1/n+1 (ax + b) ^n+1 + C

Question 2

integral of e^x

Answer 2

e^x + C

Question 3

integral of e^kx

Answer 3

1/k e^kx + C

Question 4

integral of 1/x

Answer 4

ln|x| + C

Question 5

integral of sinx

Answer 5

-cosx + C

Question 6

integral of cosx

Answer 6

sinx + C

Question 7

integral of sec^2x

Answer 7

tanx + C

Question 8

integral of sinkx

Answer 8

• 1/k coskx + C

Question 9

integral of coskx

Answer 9

1/k sinkx + C

Question 10

integral of sec^2kx

Answer 10

1/k tankx + C

Question 11

integral of f ‘(x) / f(x)

Answer 11

ln|f(x)| + C