Fundamentals of Electromagnetic Fields

Appendix E: Some Standard Formulae of Integration of Functions

  1. ? adx= ax

  2. ? a f(x)dx=a ? f(x)dx

  3. ?( u+ v) dx= ? udx+ ? vdx, where u and v are any functions of x

  4. ? udv= u ? dv ?? vdu= uv ? ? vdu

  5. , except n= ?1

  6. , (df(x) =f ?(x)dx)

  7. , (df(x) =f ?(x)dx)

  8. ? e x dx= e x

  9. , ( b>0)

  10. ? log xdx=x log x ?x

  11. ?a x log a dx=a x, ( a>0)

FORMS CONTAINING (a+bx)

For forms containing a+bx, but not listed in the table, the substitution may prove helpful.

  1. , ( n ??1)

  2. , ( n ??1, ?2)

  3. , n ?1, 2.

  4. , n ?1, 2, 3

FORMS CONTAINING c 2 x 2, x 2 ? c 2

  1. , ( c 2> x 2)

  2. , ( x 2> c 2)

FORMS CONTAINING a+ bx and c+ dx, u= a+ bx, v= c+ dx, k= ad ?bc

If k=0, then .

FORMS CONTAINING ( a+ bx n)

  1. , ( ab>0)

FORMS CONTAINING c 3 x 3

FORMS CONTAINING c 4 x 4

FORMS CONTAINING ( a+ bx+ cx 2) X= a+ bx+ cx 2 and q

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