Integration

Question 1

∫ x^n dx

Answer 1

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

Question 2

∫ 1/x dx

Answer 2

log|x| + C

Question 3

∫ e^x dx

Answer 3

e^x + C

Question 4

∫ a^x dx

Answer 4

a^x / loga + C

Question 5

∫ sinxdx

Answer 5

-cosx + C

Question 6

∫sec²x dx

Answer 6

tanx + C

Question 7

∫cosx dx

Answer 7

sinx + C

Question 8

∫cosec²x dx

Answer 8

-cotx + C

Question 9

∫tanx dx

Answer 9

-ln|cosx| + C

OR

ln|secx| + C

Question 10

∫cotx dx

Answer 10

ln|sinx| + C

Question 11

∫secx dx

Answer 11

ln|secx + tanx| + C

OR

ln|tan(π/4 + x/2)| + C

Question 12

∫cosecx dx

Answer 12

ln|cosecx - cotx| + C

Question 13

∫secxtanx dx

Answer 13

secx +C

Question 14

∫1/√(a²-x²) dx

Answer 14

sin-¹(x/a) + C

Question 15

∫1/a²+x² dx

Answer 15

1/a tan-¹(x/a) +C

Question 16

∫1/x√(x²-a²) dx

Answer 16

1/a sec-¹(x/a) + C

Question 17

∫1/x√(x²-a²) dx

Answer 17

1/a sec-¹(x/a) + C