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Text File  |  1992-04-12  |  1KB  |  33 lines
  1. inte((1/(x+x^2))*d(x)) = ln(x/(1+x))
  2. inte((1/(x+x^n))*d(x)) = ln(x^(n-1)/(1+x^(n-1)))/n
  3.  
  4. inte((x^n*ln(x))*d(x)) = x^(n+1)*((n+1)*ln(x)-1)/(n+1)^2
  5. inte(ln(x)/x*d(x)) = ln(x)^2/2
  6. inte(ln(x)^n/x*d(x)) = ln(x)^(n+1)/(n+1)
  7.  
  8. inte(sqrt(1+x^2)*d(x)) = x*sqrt(1+x^2)/2+(1/2)*ln(x+sqrt(1+x^2))
  9. inte(x^2*sqrt(1+x^2)*d(x)) = x*(1+2*x^2)*sqrt(1+x^2)/8-(1/8)*ln(x+sqrt(1+x^2))
  10. inte(sqrt(1+x^2)/x*d(x)) = sqrt(1+x^2)-ln((1+sqrt(1+x^2))/x)
  11. inte(sqrt(1+x^2)/x^2*d(x)) = ln(x+sqrt(1+x^2))-sqrt(1+x^2)/x
  12. inte(sqrt(1-x^2)*d(x)) = x*sqrt(1-x^2)/2+asin(x)/2
  13. inte(sqrt(x^2-1)*d(x)) = x*sqrt(x^2-1)/2-ln(x+sqrt(x^2-1))/2
  14.  
  15. inte((sin(x)^2)*d(x)) = x/2-sin(2*x)/4
  16. inte((cos(x)^2)*d(x)) = x/2+sin(2*x)/4
  17. inte((tan(x)^2)*d(x)) = tan(x)-x
  18. inte((cot(x)^2)*d(x)) = -cot(x)-x
  19.  
  20. inte(sin(x)*exp(x)*d(x)) = (sin(x)-cos(x))*exp(x)/2
  21. inte(cos(x)*exp(x)*d(x)) = (sin(x)+cos(x))*exp(x)/2
  22.  
  23. inte(exp(x)/x*d(x)) = Ei(x)
  24. inte(sin(x)/x*d(x)) = Si(x)
  25. inte(cos(x)/x*d(x)) = Ci(x)
  26.  
  27. inte((sin(x)^n)*d(x)) = -sin(x)^(n-1)*cos(x)/n+((n-1)/n)*inte((sin(x)^(n-2))*d(x))
  28. inte((cos(x)^n)*d(x)) = sin(x)*cos(x)^(n-1)+((n-1)/n)*inte((cos(x)^(n-2))*d(x))
  29. inte((tan(x)^n)*d(x)) = tan(x)^(n-1)/(n-1)-inte((tan(x)^(n-2))*d(x))
  30. inte((cot(x)^n)*d(x)) = -cot(x)^(n-1)/(n-1)-inte((cot(x)^(n-2))*d(x))
  31.  
  32. end
  33.