Integrale

Question 1

S x^n dx

Answer 1

X^n+1/ n+1 +C

Question 2

S a^x dx

Answer 2

a^x/ ln a +C

Question 3

S e^x dx

Answer 3

e^x +C

Question 4

S 1/x dx

Answer 4

ln |x| +C

Question 5

S 1/x+-a dx

Answer 5

ln |x+-a| +C

Question 6

S 1/ \/x²+a² dx

Answer 6

ln (x+ \/x²+a²) +C

Question 7

S 1/ \/x²-a² dx

Answer 7

ln |x+ \/x²-a²| +C

Question 8

S 1/x²+a² dx

Answer 8

1/a • arctg x/a +C

Question 9

S 1/x²-a² dx

Answer 9

1/2a • ln|x-a/x+a|+ C

Question 10

S sin x dx

Answer 10

-cos x +C

Question 11

S cos x dx

Answer 11

sin x

Question 12

S 1/cos²x dx

Answer 12

tg x

Question 13

S 1/sin²x dx

Answer 13

-ctg x

Question 14

S tg x dx

Answer 14

-ln |cos x| +C

Question 15

S ctg x dx

Answer 15

ln |sin x| +C

Question 16

S 1/ \/a²-x² dx

Answer 16

arcsin x/a +C

Question 17

S x/ \/x²+-a² dx

Answer 17

\/ x²+-a² +C

Question 18

S dx

Answer 18

x +C

Question 19

S n dx

Answer 19

nx +C

Question 20

S a/x dx

Answer 20

a • ln |x| +C

Question 21

S f’(x) dx

Answer 21

f(x)

Question 22

S cos ax dx

Answer 22

sin ax/a +C

Question 23

S e^ax dx

Answer 23

e^ax/a +C

Question 24

S f’(x)/ f(x) dx

Answer 24

ln |f(x)| +C

Question 25

sin 2x

Answer 25

2 sinx cosx

Question 26

cos 2x

Answer 26

cos²x-sin²x 2cos²x-1 1-2sin²x