Integration Formulas – HSC Math

Posted In: Mathematics
  1. $∫1/\x\ \dx=ln|x|+c$
  2. $∫e^{mx}\ \dx=1/m\ e^{mx}+c$
  3. $∫a^xd^x\ \dx=a^x/{ln\ a}+c, a>0, a≠1$
  4. $∫cos\ x\ \dx=sin\ x+c$
  5. $∫sin\ x\ \dx=-cos\ x+c$
  6. $∫sec^2\ x\ \dx=tan\ x+c$
  7. $∫cosec^2\ x\ \dx=-cot\ x+c$
  8. $∫sec\ x\ tan\ x\ \dx=sec\ x+c$
  9. $∫cosec\ x\ cot\ x\ \dx=-cosec\ x+c$
  10. $∫tan\ x\ \dx=-ln|cos\ x|+c=ln|sec\ x|+c$
  11. $∫cot\ x\ \dx=ln|sin\ x|+c$
  12. $∫sec\ x\ \dx=ln|tan(π/4+x/2)|+c$
  13. $∫sec\ x\ \dx=ln|sec\ x+tan\ x|+c$
  14. $∫cosec\ x\ \dx=ln|tan(x/2)|+c$
  15. $∫cosec\ x\ \dx=ln|cosec\ x-cot\ x|+c$
  16. $∫{f'(x)}/{f(x)} \dx=ln|f(x)|+c$
  17. $∫{f'(x)}/√{f(x)} \dx=2√{f(x)}+c$
  18. $∫{dx}/{a^2+x^2}=1/a\ tan^{-1}x/a+c$
  19. $∫{dx}/{a^2-x^2}=1/{2a}\ ln\ {{a+x}/{a-x}}+c$
  20. $∫{dx}/{x^2-a^2}=1/{2a}\ ln\ {{x-a}/{x+a}}+c$
  21. $∫{dx}/√{a^2-x^2}=sin^{-1}x/a+c$
  22. $∫{dx}/√{a^2+x^2}=ln|√{a^2+x^2}+x|+c$
  23. $∫{dx}/√{x^2-a^2}=ln|√{x^2-a^2}+x|+c$
  24. $∫√{a^2-x^2}\ dx={x√{a^2-x^2}}/2+a^2/2\ sin^{-1}x/a+c$
  25. $∫uv\ dx=u∫v\ dx-∫\{{du}/{dx}∫v\ dx\}dx$

Post Tags: HSC | Integration


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