Table of Standard Integrals - University of Sydney

Table of Standard Integrals

1. xn dx = xn+1 + C (n = -1) n+1

dx

2.

= ln |x| + C

x

9. sec2 x dx = tan x + C 10. cosec2 x dx = - cot x + C

3. ex dx = ex + C

11. sec x dx = ln sec x + tan x + C

4. sin x dx = - cos x + C

12. cosec x dx = ln cosec x - cot x + C

5. cos x dx = sin x + C

13. sinh x dx = cosh x + C

6. tan x dx = - ln cos x + C

14. cosh x dx = sinh x + C

7. cot x dx = ln sin x + C

15. tanh x dx = ln cosh x + C

8.

dx = 1 tan-1 x + C

a2 + x2 a

a

16. dx = sin-1 x + C (|x| < a)

a2 - x2

a

17.

dx

= sinh-1 x

+ C = ln x + x2 + a2

+C

x2 + a2

a

18.

dx

= cosh-1 x

+ C = ln x + x2 - a2

+C

(x > a)

x2 - a2

a

Linearity: f (x) + ?g(x) dx = f (x) dx + ? g(x) dx

Integration by substitution:

du f (u(x)) dx = f (u) du

dx

Integration by parts: f (x)g (x) dx = f (x)g(x) - f (x)g(x) dx

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