Integrals

Question 1

∫kf(u) du

Answer 1

k ∫f(u) du

Question 2

∫[f(u) +- g(u)] du

Answer 2

∫f(u) du +- ∫g(u) du

Question 3

∫du

Answer 3

u+C

Question 4

∫u^n du

Answer 4

(u^n+1 / n+1) +C n no equal -1

Question 5

∫du/u

Answer 5

Ln |u| + C

Question 6

∫e^u du

Answer 6

e^u +C

Question 7

∫a^u du

Answer 7

(1/ln(a))a^u +C

Question 8

∫cos(u) du

Answer 8

sin(u) +C

Question 8

∫sin(u) du

Answer 8

-cos(u) +C

Question 9

∫tan(u) du

Answer 9

-ln|cos u| + C

Question 10

∫cot(u) du

Answer 10

ln|sin(u)| + C

Question 11

∫sec(u) du

Answer 11

ln|sec(u) + tan(u)| + C

Question 12

∫csc(u) du

Answer 12

-ln|csc(u) + cot(u)| +C

Question 13

∫sec^2(u) du

Answer 13

tan(u) +C

Question 14

∫csc^2(u) du

Answer 14

-cot(u) + C

Question 15

∫sec(u)tan(u) du

Answer 15

sec(u) + C

Question 16

∫csc(u)cot(u) du

Answer 16

-csc(u) +C

Question 17

∫du / root(a^2 - u^2)

Answer 17

arcsin(u/a) + C

Question 18

∫du /a^2+u^2

Answer 18

(1/a)arctan(u/a) + C

Question 19

∫ du / u(root(u^2-a^2))

Answer 19

(1/a)(arcsec((|u|/a)) + C