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VUT Calculus III formula sheet, Cheat Sheet of Mathematics

Vaal University of TechnologyMathematics

Formula sheet to be used for calculus III provided by vut

Typology: Cheat Sheet

2021/2022

Uploaded on 08/28/2024

emile-santos-9
emile-santos-9 🇿🇦

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APPENDIX 1: INTEGRATION LIST
1. ′
() ()
=
()
[]
+
+≠
∫
+
fxfx dx x
n
cn
nn
f1
1
1;
2. ′
()
()
=
()
+
∫
fx
fx dx fx c ln
3. ′
()
=+
()
()
∫
fxadxa
ac
fx
fx
ln
4. ′
()
=+
() ()
∫
fxedxe c
fx fx
5. ′
() ()
=
()
+
∫
fx fxdx fx ccossin
6. ′
() ()
=−
()
+
∫
fx fxdx fx csi
nc
os
7. ′
() ()
=
()
+
∫
fx fxdx fx csectan
2
8. ′
() ()
=−
()
+
fx fxdx fx ccose cotc2
9. ′
() () ()
=
()
+
∫
fx fx fxdx fx cse
cs
ectan
10. ′
() () ()
=−
()
+
∫
fx fx fxdx fx ccoseccot cosec
11. ′
() ()
=
()
+
∫
fx fxdx fx ctanlnsec
12. ′
() ()
=
()
+
∫
fx fxdx fx ccotlnsin
13. ′
() ()
=
()
+
()
+
∫
fx fxdx fx fx cseclntansec
14. ′
() ()
=
()
−
()
+
∫
fx fxdx fx fx ccoseccosecln cot
15. ′
() ()
=
()
+
∫
fx fxdx fx ccosh sinh
16. ′
() ()
=
()
+
∫
fx fxdx fx csinh cosh
17. ′
() ()
=
()
+
∫
fx fxdx fx csectanhh2
Maths for ES appendices.indd 165 2016/11/25 08:29:16 AM
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Download VUT Calculus III formula sheet and more Cheat Sheet Mathematics in PDF only on Docsity!

APPENDIX 1: INTEGRATION LIST

1. ′( )  ( ) = [^ (^ )]

∫ +^ ≠

f x f x dx x n

c n n (^) f n^1 1

∫ =^ (^ ) +

f x f x dx lnf x c

3. ′( ) (^ )^ = +

( ) ∫ f^ x a^ dx^

a a

f x c f x ln

  1. (^) ∫ f ′( x e) f^ (^ x)^ dx = e f^ (^ x)+c
  2. (^) ∫ f ′( x) cos f (^) ( x dx) = sinf (^) ( x (^) ) +c
  3. (^) ∫ f ′( x) sin f (^) ( x dx) = − cosf (^) ( x (^) ) +c
  4. (^) ∫ f ′( x) sec 2 f (^) ( x dx) = tanf (^) ( x (^) ) +c
  5. (^) ∫ f ′( x) cose c 2 f (^) ( x dx) = − cotf (^) ( x (^) ) +c
  6. (^) ∫ f ′( x) sec f (^) ( x) tanf (^) ( x dx) = secf (^) ( x) + c
  7. (^) ∫ f ′( x) cosec f (^) ( x) cot f (^) ( x dx) = − cosecf (^) ( x (^) ) +c
  8. (^) ∫ f ′( x) tan f (^) ( x dx) = ln secf (^) ( x) + c
  9. (^) ∫ f ′( x) cot f (^) ( x dx) = ln sinf (^) ( x (^) ) +c
  10. (^) ∫ f ′( x) sec f (^) ( x dx) = ln secf (^) ( x (^) ) + tanf (^) ( x (^) ) +c
  11. (^) ∫ f ′( x) cosec f (^) ( x dx) = ln cosecf (^) ( x (^) ) − cotf (^) ( x) + c
  12. (^) ∫ f ′( x) cosh f (^) ( x dx) = sinhf (^) ( x (^) ) +c
  13. (^) ∫ f ′( x) sinh f (^) ( x dx) = coshf (^) ( x (^) ) +c
  14. (^) ∫ f ′( x) sec h 2 f (^) ( x dx) = tanhf (^) ( x (^) ) +c

166 STUDENTS ENGINEERINGMATICS FORMATHE

18. ∫ f ′( x) cosec h 2 f ( x dx) = − cothf ( x ) +c

19. ∫ f ′( x) sec h f ( x ) tanh f ( x dx) = − sechf ( x) + c

20. ∫ f ′( x) cosec h f ( x) coth f ( x dx) = − cosechf ( x ) +c

21. ∫ f ′( x) tanh f ( x dx) = ln coshf ( x ) +c

22. ∫ f ′( x) coth f ( x dx) = ln sinhf ( x ) +c

23. ′(^ )
− [ ( )]

∫ f^ x =^ −^ (^ ) +^ −^ − (^ ) +

a f x

dx f x a c f x a 2 2 sin^1 or cos^1 c

24. ′(^ )
[ ( )] +

∫ f^ x =^ − (^ ) +

f x a

dx f^ x a 2 2 sinh^1 cor^ ln^ f^ (^ x)^ (^ ) a

f x a

+ ( ) + c

2 1

25. ′(^ )
[ (^ )] −

∫ f^ x − +

f x a

dx f x a 2 2 cosh^1 cor^ ln^

f x a

f x a

( ) + ( ( )) − c

2 1

26. ′(^ )
[ ( )] +

∫ f^ x =^ − (^ ) +

f x a

dx a

f x a 2 2 1 tan^1 cor^ −^

a

f x a

cot c

27. ′(^ )
− [ ( )]

∫ f^ x =^ − (^ ) +

a f x

dx a

f x a 2 2 1 tanh^1 cor^1 2 a

a f x a f x

ln +^ (^ ) c

28. ′(^ )
[ ( )] −

f x f x a

dx a

f x a 2 2 1 coth^1 cor^1 2 a

f x a f x a

ln (^ )^ − c

29. ′( ) − [ ( )] =  ( ) − [ ( )] + (^ ) +
^

∫ f^ x^ a^ f^ x^ dx^ f^ x^ a^ f^ x^ a^ − f^ x +

a

(^2 2 12 2 2 1) c 2 sin

30. ′( ) [ ( )] + =  ( ) [ ( )] + + (^ ) +
^

∫ f^ x^ f^ x^ a^ dx^ f^ x^ f^ x^ a^ a^ − f^ x +

a

sinh cc

31. ′( ) [ ( )] − =  ( ) [ ( )] − − (^ ) +
^

∫ f^ x^ f^ x^ a^ dx^ f^ x^ f^ x^ a^ a^ − +

f x a

cosh cc

32. ∫ u dv = uv −∫v du