High School Calculus/Integration by Parts

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i would like to make life easy for the junior mathematicians in integration by parts.There is a bit trouble on the choice of the variable "U" in integration by parts,because some students tend to vice verse their U and V when using integration by parts,how ever i will like to tell a certain story which reads as follows;


there was a certain discussion which was made between the zimbabwean maths pupils and the egyptian maths pupils some time long back.When this discussion went on and on conflict arose between the two groups and the zimbabwean pupils analysed the conflict from bottom to top very well ,and they realised that but it seems as if the "EGYPTIAN PUPILS ARE LAZY TO THINK",

THE POINT IS: WHEN YOU ARE A GIVEN A FUNCTION TO INTEGRATE BY PARTS (PRODUCT OF CAUSE) WE WIL USE ;

L-----AZY are P-----UPILS E-----GYIPTIAN;

WE READ THIS FROM BOTTOM TO TOP AS EGYPIAN PUPILS are LAZY


WHERE E----- EXPONENTIAL; L-----LOGARITHM; P-----POLYNOMIAL; . SO WHEN EVER WE ARE GIVEN A FUNCTION TO INTEGRATE BY PARTS WE FIRST CHECK WHETHER THER IS A LOGARITHM EG (lnx),IF IT IS THERE IT WILL BE OUR "U",IF NOT WE MOVE ON TO CHECK FOR THE POLYNOMIAL FUNCTION (X,2X,X^2,X^3 ETC), IF THERE THEN THAT WILL BE OUR U.IF NO WE CHOSE EXPONENTIAL (e^x) ,AS OUR U.IN THIS ORDER. IT CAN BE SEEN THAT HERE TRIG FUNCTION WILL NEVER BE U, THIS CAN BE TRIED BY EXAMPLES AND DEFINITELY WE ARE NOW GOING TO WIN OUR INTEGRATION BY PARTS ,JUST AS EASY AS IT IS NOW

Other Problems to Work On[edit]

Ex. 2

\int \cos (x) x^2 \operatorname {d}x

Ex. 3

\int \arcsec (x) \left (\frac {1}{x} \right) \operatorname {d}x