Standard Integrals (ax + b)

Question 1

INTEGRATE

xⁿ

Answer 1

(1/n+1) * x⁽ⁿ⁺¹⁾ + C

Question 2

INTEGRATE

e^x

Answer 2

e^x +C

Question 3

INTEGRATE

1 / x

Answer 3

ln | x | + C

Question 4

INTEGRATE

sin x

Answer 4

• cos x + C

Question 5

INTEGRATE

cos x

Answer 5

sin x + C

Question 6

INTEGRATE

sec² x

Answer 6

tan x + C

Question 7

INTEGRATE

1 / √(1 - x²)

Answer 7

sin^-1 x + C

Question 8

INTEGRATE

• 1 / √(1 - x²)

Answer 8

cos^-1 x + C

Question 9

INTEGRATE

1 / (1 + x²)

Answer 9

tan^-1 x + C

Question 10

INTEGRATE

tan x

Answer 10

• ln (cos x) + C

Question 11

INTEGRATE

sinh x

Answer 11

cosh x + C

Question 12

INTEGRATE

cosh x

Answer 12

sinh x + C

Question 13

INTEGRATE

sech² x

Answer 13

tanh x + C

Question 14

INTEGRATE

1 / √(1 + x²)

Answer 14

sinh^-1 x + C

Question 15

INTEGRATE

1 / √( -1 + x² )

Answer 15

cosh^-1 x + C

Question 16

INTEGRATE

1 / ( 1 - x²)

Answer 16

tanh^-1 x + C

Question 17

For Standard Integrals,

a, b, C and n =/= -1 are … .

Answer 17

constants

Question 18

INTEGRATE

(ax + b)ⁿ

Answer 18

1/a * 1/(n+1) * (ax + b)ⁿ⁺¹ + C

Question 19

INTEGRATE

e^{(<em>ax + b</em>)}

Answer 19

1/a * e^{(<em>ax + b</em>)} + C

Question 20

INTEGRATE

1 / (ax + b)

Answer 20

1/a * ln | ax + b | + C

Question 21

INTEGRATE

sin (ax + b)

Answer 21

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

Question 22

INTEGRATE

cos (ax + b)

Answer 22

1/a sin(ax + b) + C

Question 23

INTEGRATE

sec² (ax + b)

Answer 23

1/a tan(ax + b) + C

Question 24

INTEGRATE

1 / √(1 - (ax + b)² )

Answer 24

1/a sin^-1 (ax + b) + C

Question 25

INTEGRATE - 1 / √(1 - (ax + b)²)

Answer 25

1/a cos^-1 (*ax + b*) + C

Question 26

INTEGRATE 1 / (1 + (ax + b)²)

Answer 26

1/a tan^-1 (*ax + b*) + C

Question 27

INTEGRATE tan (ax + b)

Answer 27

-1/a ln( cos(*ax+b*) ) + C

Question 28

INTEGRATE sinh (*ax + b*)

Answer 28

1/a cosh (*ax + b*) + C

Question 29

INTEGRATE cosh (*ax + b*)

Answer 29

1/a sinh (*ax + b*) + C

Question 30

INTEGRATE sech² (*ax + b*)

Answer 30

1/a tanh (*ax + b*) + C

Question 31

INTEGRATE 1 / √(1 + (*ax + b*)²)

Answer 31

1/a sinh^-1 (*ax + b*) + C

Question 32

INTEGRATE 1 / √(-1 + (ax + b)2)

Answer 32

1/a cosh^-1 (*ax + b*) + C

Question 33

INTEGRATE 1 / (1 - (*ax + b*)²)

Answer 33

1/a tanh^-1 (*ax + b*) + C