Integration

Question 1

d/dx integral f(x) dx

Answer 1

f(x)

Question 2

Integral dF(x)

Answer 2

F(x) + c

Question 3

Integral cf(x) dx

Answer 3

c integral f(x) dx

Question 4

integral (f(x) +/- g(x)) dx

Answer 4

Integral f(x) dx +/- integral g(x) dx

Question 5

Integral between a and b f(x) dx

Answer 5

• integral between b and a f(x) dx

Question 6

Integral between a and a f(x) dx

Answer 6

0

Question 7

Integral between a and b cf(x) dx

Answer 7

c integral between a and b f(x) dx

Question 8

Integral between a and c f(x) dx + integral between c and b f(x) dx

Answer 8

Integral between a and b f(x) dx

Question 9

Integral dx

Answer 9

x + C

Question 10

Integral x^(n) dx

Answer 10

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

Question 11

Integral dx/x

Answer 11

ln |x| + C

Question 12

Integral dx/(1 + x^2)

Answer 12

arctanx + C

Question 13

Integral dx/(1-x^2)^1/2

Answer 13

arcsinx + c

Question 14

Integral e^x dx

Answer 14

e^x + C

Question 15

Integral a^x dx

Answer 15

a^x/ln(a) + C

Question 16

Integral sinx dx

Answer 16

• cosx + C

Question 17

Integral cosx dx

Answer 17

sinx + C

Question 18

Integral dx/(cos^(2)x)

Answer 18

tanx + C

Question 19

Integral dx/(sin^(2)x)

Answer 19

• cotx + C

Question 20

Integral sinhx dx

Answer 20

coshx + C

Question 21

Integral coshx

Answer 21

sinhx + c

Question 22

Integral dx/(cosh^(2)x)

Answer 22

tanhx + C

Question 23

Integral dx/(sinh^(2)x)

Answer 23

cothx + C

Question 24

Integral dx/(1 - x^(2))

Answer 24

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

Question 25

Integral dx/(x^(2) +/- 1)^1/2

Answer 25

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

Question 26

Possible substitutions for (a^(2) - x^(2))^1/2

Answer 26

x = asinu or x = atanhu

Question 27

Possible substitutions for (a^(2) + x^(2))^1/2

Answer 27

x = asinhu or x = atanu

Question 28

Possible substitutions for (x^(2) - a^(2))^1/2

Answer 28

x = acoshu or x = a/cosu

Question 29

Possible substitutions for trigonometric functions

Answer 29

u = tan(x/2) or u = sinx or u = cosx

Question 30

Possible substitutions for hyperbolic functions

Answer 30

u = e^x or u = sinhx or u = coshx or u = tanh(x/2)