Kamis, 28 Mei 2015

Rumus Dasar Integral Taktentu



Berikut ini adalah rumus-rumus dasar integral taktentu:
  1. \int \,{\rm d}x = x + C
  2. \int x^n\,{\rm d}x = \frac{x^{n+1}}{n+1} + C\qquad\mbox{ jika }n \ne -1
  3. \int {dx \over x} = \ln{\left|x\right|} + C
  4. \int {dx \over {a^2+x^2}} = {1 \over a}\arctan {x \over a} + C
  5. \int e^x\,dx = e^x + C
  6. \int a^x\,dx = \frac{a^x}{\ln{a}} + C
  7. \int \sin{x}\, dx = -\cos{x} + C
  8. \int \cos{x}\, dx = \sin{x} + C
  9. \int \tan{x} \, dx = \ln{\left| \sec {x} \right|} + C
  10. \int \cot{x} \, dx = -\ln{\left| \csc{x} \right|} + C
  11. \int \sec{x} \, dx = \ln{\left| \sec{x} + \tan{x}\right|} + C
  12. \int \csc{x} \, dx = -\ln{\left| \csc{x} + \cot{x}\right|} + C
  13. \int \sec^2 x \, dx = \tan x + C
  14. \int \csc^2 x \, dx = -\cot x + C
  15. \int \sec{x} \, \tan{x} \, dx = \sec{x} + C
  16. \int \csc{x} \, \cot{x} \, dx = - \csc{x} + C
  17. \int \sin^2 x \, dx = \frac{1}{2}(x - \sin x \cos x) + C
  18. \int \cos^2 x \, dx = \frac{1}{2}(x + \sin x \cos x) + C
  19. \int \sec^3 x \, dx = \frac{1}{2}\sec x \tan x + \frac{1}{2}\ln|\sec x + \tan x| + C
  20. \int \sin^n x \, dx = - \frac{\sin^{n-1} {x} \cos {x}}{n} + \frac{n-1}{n} \int \sin^{n-2}{x} \, dx
  21. \int \cos^n x \, dx = \frac{\cos^{n-1} {x} \sin {x}}{n} + \frac{n-1}{n} \int \cos^{n-2}{x} \, dx
  22. \int \arctan{x} \, dx = x \, \arctan{x} - \frac{1}{2} \ln{\left| 1 + x^2\right|} + C
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