Expert: Sherry Wallin - 1/20/2009

Question
QUESTION: How to Integrate this ((x)/(x+2)^3) by parts. Much appreciated

ANSWER: Hi Qi~
    Is there some reason (like in the problem statement or required as an instruction by your teacher or you just want to see an integration by parts problem) that you want to integrate by parts? It isn't necessary because you can use partial fractions but nonetheless I will show you how to integrate this function by parts. It will be attached in an image file. Please let me know if you can not view it or if you have any further questions.

Math Prof


Qi, you are right I did not add the constant! Thanks for reminding me and you are welcome as well.

---------- FOLLOW-UP ----------

QUESTION: How come ((x(x+2)^-2)/-2)+((x+2)^-1)/-2) multiply with (x+2)^2/(x+2)^2? I dont understand & how do you know it is multiply by (x+2)^2/(x+2)^2? The only difference between my working and yours is that i dont multiply with (x+2)^2/(x+2)^2. Thanks you

Answer
multiplying by (x+2)2/(x+2)^2 is just 1 and I chose it because I had
((x(x+2)^-2)/-2)+((x+2)^-1)/-2) and it made the (x(x+2)^-2) go away and
(x+2)^-1) into x+2 in the numerator. There are other ways to do this problem but the way I did it is the most efficient. When there are common factors to a negative power in the numerator always multiply top and bottom by the positive power of the largest absolute value of the negative value to get the negative exponents to go away.

Math Prof