Integration formulae
(px+q) / (ax² + bx +c) , (px+q) /sqrt(ax² + bx +c) ,
(px² + qx +r) /(ax² + bx +c) type
(psinx+qcosx ) / (a sinx + b cosx )
----------------------------------------------------------------------------
for
---------------------------------------
you might then have to restore to completion of squares in some cases after the manipulationin some cases the manipulation can be done through inspection
Examples
* ∫ { (4x - 7) / (x² + x +1)} dx
integration of linear expression in numerator mixed with quadratic expression
* ∫ { cosx/ [ sinx +cosx] } dx
integral of [ cos x ] / [sin x + cos x ]
*not the above types but still an example of manupulating the angle in the numerator in terms of the angles in the denominator
integral of 1 / [cos(x+a)cos(x+b)]
*integral of { (cos x)^2 / [ (cos x)^2+ 4 (sin x)^2 ] }
answer and a little explanation of integral of { (cos x)^2 / [ (cos x)^2+ 4 (sin x)^2 ] }
PAGE 1 BASIC INTEGRATION
PAGE 2 INTEGRATION BY SUBSTITUTION
PAGE 3 INTEGRATION BY COMPLETION OF SQUARES
PAGE 4 INTEGRATION BY PARTS
PAGE 5 INTEGRATION BY MANIPULATION OF NUMERATOR IN TERMS OF DENOMINATOR
-----------------------------------------------------------
please leave your comments below
------------------------------------------------------------
index of math problems
disclaimer:
There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work
No comments:
Post a Comment
please leave your comments