integration

Question 1

h’(x) / h(x) dx

Answer 1

ln|h(x)| + C

Question 2

a tan (kx) dx

Answer 2

a/k ln|sec (kx)| + C

Question 3

a cot (kx) dx

Answer 3

a/k ln|sin (kx) + C

Question 4

a sec^2 (kx) dx

Answer 4

a/k tan (kx) + C

Question 5

a sec (kx) tan (kx) dx

Answer 5

a/k sec (kx) + C

Question 6

a csc (kx) cot (kx) dx

Answer 6

-a/k csc (kx) + C

Question 7

a csc^2 (kx) dx

Answer 7

-a/k cot (kx) + C

Question 8

a ln (kx) dx

Answer 8

a (x ln (kx) - x) + C

Question 9

sin-1 (x) dx

Answer 9

x sin-1 (x) + root(1-x^2) + C

Question 10

tan-1 (x) dx

Answer 10

x tan-1 (x) - 1/2 ln|x^2 +1| + C