The discussion revolves around integrating rational functions with unfactorable denominators, specifically the integrals of xdx/(x^2 + 4x + 5) and xdx/sqrt(x^2 + 4x + 13). Participants are exploring methods for integration and addressing challenges related to the problem setup.
The conversation is ongoing, with participants offering guidance on rewriting the integrals and exploring different approaches. There is a focus on ensuring that the original poster engages with the material rather than receiving direct answers.
Some participants emphasize the importance of not factoring the denominator, as it is unfactorable, and suggest completing the square instead. There are also language barriers noted, particularly regarding the terminology used in integration methods.
That's not the way it works here. We will help you with your homework, but we will not do it for you. You have to put some effort in.Hamid1 said:Yes,I want the method.
can you explain more?rewrite the numerator as (2x+4-4)/2.Try splitting the integral into two functions now.
I have solved about 100 integrals but I can't do these two.I don't know the method.That's not the way it works here. We will help you with your homework, but we will not do it for you. You have to put some effort in.
Thank you.the first part is easy to solve but how can I solve the second part?virus said:rewrite as integral of 1/2*( 2x+4/x^2+4x+5) -2*integral of (1/x^2+4x+5) . Now try to solve both of these integrals separately.
Use partial fractions.Hamid1 said:Thank you.the first part is easy to solve but how can I solve the second part?
Since you have "xdx" in the numerator- which should remind you of the derivative of x2, you should immediately think about getting the denominator in the form "x2- a" so you can substitute. In other words, start by completing the square in the denominator.Hamid1 said:Hi all.
can anyone integrate xdx/x^2+4x+5
and this one : xdx/sqrt(x^2+4x+13)
thank you and excuse me for english:)
Can you tell me how?Because I don't know english(partial fractions) very well.Hootenanny said:Use partial fractions.
Can you factorise the denominator and then split the fraction into two different fractions?Hamid1 said:Can you tell me how?Because I don't know english(partial fractions) very well.
Whoops! I thought the denominator was (x2-4x-5).HallsofIvy said:No, the whole point of this problem is that you cannot factor the denominator. Complete the square instead.