Matematika Education: Integral Kalkulus Bentuk Trigonometri

$1. \int Sin u du = -Cos u + C$

$2. \int Cos u du = Sin u + C$

$3. \int Tan u du = -ln \left | Cos \right u|+ C$

$4. \int Cot u du = ln \left | Sin \right u|+ C$

$5. \int Sec u du = ln \left | Sec u \right + Tan u|+ C$

$6. \int Csc u du = ln \left | Csc u \right - Cot u|+ C$

$7. \int Sec^{2} u du = Tan u + C$

$8. \int Csc^{2} u du = -Cot u + C$

$9. \int Sec u Tan u du = Sec u + C$

$10. \int Csc u Cot u du = -Csc u + C$

$11. \int Sin^{2}udu=\frac{1}{2}u-\frac{1}{4}Sin 2u + C$

$12. \int Cos^{2}udu=\frac{1}{2}u+\frac{1}{4}Sin 2u + C$

$13. \int Tan^{2}udu=Tan u -u + C$

$14. \int Cot^{2}udu=-Cot u -u + C$

$15. \int Sin^{3}udu=-\frac{1}{3}\left ( 2+ \right Sin^{2} u) Cos u+ C$

$16. \int Cos^{3}udu=\frac{1}{3}\left ( 2+ \right Cos^{2} u) Sin u+ C$

$17. \int Tan^{3}udu=\frac{1}{2}Tan^{2}u+ ln \left | Cos \right u|+ C$

$18. \int Cot^{3}udu=-\frac{1}{2}Cot^{2}u- ln \left | Sin \right u|+ C$

$19. \int sec^{3}udu=\frac{1}{2}Secu Tan u+\frac{1}{2}ln\left | Secu \right+Tanu |+ C$

$20. \int Csc^{3}udu=-\frac{1}{2}Cscu Cot u+\frac{1}{2}ln\left | Cscu \right-Cotu |+ C$

$21. \int Sin au Sin bu du=\frac{Sin\left ( a- \right b)u}{2\left ( a- \right b)}-\frac{Sin\left ( a+ \right b)u}{2\left ( a+ \right b)} + C, Jika a^{2}\neq b^{2}$

$22. \int Cos au Cos bu du=\frac{Sin\left ( a- \right b)u}{2\left ( a- \right b)}+\frac{Sin\left ( a+ \right b)u}{2\left ( a+ \right b)} + C, Jika a^{2}\neq b^{2}$

$23. \int Sin au Cos bu du=-\frac{Cos\left ( a- \right b)u}{2\left ( a- \right b)}-\frac{Cos\left ( a+ \right b)u}{2\left ( a+ \right b)} + C, Jika a^{2}\neq b^{2}$

$24. \int Sin^{n}udu=-\frac{1}{n}Sin^{n-1}u Cos u +\frac{n-1}{n}\int Sin^{n-2}u du$

$25. \int Cos^{n}udu=\frac{1}{n}Cos^{n-1}u Sin u +\frac{n-1}{n}\int Cos^{n-2}u du$

$26. \int Tan^{n}udu=\frac{1}{n-1}Tan^{n-1}u -\int Tan^{n-2}u du, jika n\neq 1$

$27. \int Cot^{n}udu=\frac{-1}{n-1}Cot^{n-1}u -\int Cot^{n-2}u du, jika n\neq 1$

$28. \int Sec^{n}udu=\frac{1}{n-1}Sec^{n-2}uTan u +\frac{n-2}{n-1}\int Sec^{n-2}u du, jika n\neq 1$

$29. \int Csc^{n}udu=\frac{-1}{n-1}Csc^{n-2}uCot u +\frac{n-2}{n-1}\int Csc^{n-2}u du, jika n\neq 1$

$30. \int Sin^{n}uCos^{m}udu=-\frac{-1Sin^{n-1}u Cos^{m+1}}{n+m}+\frac{n-1}{n+m}\int Sin^{n-2}uCos^{m}udu,jika n\neq 1$

$31. \int u Sin u du = Sin u -u + C$

$32. \int u Cos u du = Cos u + u Sin u + C$

$33. \int u^{n} Sin u du = -u^{n}Cos u + n\int u^{n-1}Cos udu$

$34. \int u^{n} Cos u du = u^{n}Sin u - n\int u^{n-1}Sin udu$

1 komentar:

Unknown4 Januari 2014 pukul 01.14
Tanya mb
integral Cos^3 x dx = [cos^2 x . cos x dx --->dimana cos^2 x = (1-sin^2 x)
[(1-sin^2 x) . cos x dx
[cos x dx - [ sin^2 x cos x dx
= sin x - [sin^2 x d (cos x)
misal : u = sinx ; du = cos(x) dx
maka : sin x - [u^2 du
sin x - 1/3 u^3 +c
sin x - 1/3 sin^3 x +c

mohon pencerahan.
BalasHapus
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Selasa, 04 Januari 2011

Integral Kalkulus Bentuk Trigonometri

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