lampiran 2 kalkulus 2

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FUNGSI INTEGRAL TRIGONOMETRI

LAMPIRAN 2

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FUNGSI INTEGRAL

Sumber:1. Kholifatunnisa, Galih, dkk. 2009. Fungsi Integral

Trigonometri. Yogyakarta: UIN Sunan Kalijaga.2. Supama, dkk. 2003. Kalkulus 2. Yogyakarta:

FMIPA UGM

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TRIGONOMETRI DASAR

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FUNGSI DASAR INTEGRAL

1. ∫ dx = x + C2.

3. ∫sin x dx = -cos x +C4. ∫cos x dx = sin x + C5. ∫sec2 x dx = tan x + C6. ∫cosec2 x dx = -cotan x +C

∫

∫+=

−≠++

= +

Cxxdx

xuntukCxn

dxx nn

||ln

1_;1

1 1

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FUNGSI DASAR INTEGRAL

7. ∫sec x tan x dx = sec x + C8. ∫cosec x cotan x dx = -cosec x + C9.

10.

∫∫

+=

≠>+=

Cedxe

aaCaadxa

xx

xx 1;0;

ln

∫

+−+

=+ Cx

Cxxdx

arctanarctan

1 2

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FUNGSI DASAR INTEGRAL

11.

12.

13. ∫sinh x dx = cosh x+ C14. ∫cosh x dx = sinh x + C

+−+

=−∫ Cx

Cx

xdx

arccosarcsin

1 2

∫

+−+

=− Cecx

Cxarc

xxdx

arccossec

12

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FUNGSI DASAR INTEGRAL

15.

16.

+−

+=

−∫C

ax

Cax

xadx

arccos

arcsin

22

∫

+−

+=

+ Caxarc

a

Cax

axa

dx

cot1

arctan1

22

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FUNGSI DASAR INTEGRAL

17.

18. ∫ tan x dx = ln |sec x| + C19. ∫ cotan x dx = ln |sin x| + C20. ∫ sec x dx = ln |sec x + tan x| + C21. ∫ cosec x dx = ln |cosec x – cotan x| + C

+−

+=

−∫C

axec

a

Caxarc

aaxx

dx

arccos1

sec1

22