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monroe17
 2 years ago
integral of (3x+5)/(5x^24x+1)dx
monroe17
 2 years ago
integral of (3x+5)/(5x^24x+1)dx

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wio
 2 years ago
Best ResponseYou've already chosen the best response.1It's a rational polynomial, have you tried factoring it?

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.0let me do it real quick

AnElephant
 2 years ago
Best ResponseYou've already chosen the best response.0imaginary roots wont help you in this i think... hold on... (props for a challenging question)

wio
 2 years ago
Best ResponseYou've already chosen the best response.1You said it can't be factored... what are the roots of the denominator?

wio
 2 years ago
Best ResponseYou've already chosen the best response.1rational functions like this often don't have elementary anti derivatives.

wio
 2 years ago
Best ResponseYou've already chosen the best response.1Is this a homework problem?

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.0it's a practice problem for my exam this coming thursday. I'm trying to study and get familiar with the problems.

AnElephant
 2 years ago
Best ResponseYou've already chosen the best response.0ok got it, in this type of question you need to rewrite it so that at least one of the parts of the numerator is equal to the derivative of the denominator. So we may rewrite it like so: 31/5 integral(1/5x^24x+1) +3/10 integral((10x4)/(5x^24x+1)) Use u substitution for integral((10x4)/(5x^24x+1)) u= the denominator and du = the numerator So now you get 3/10 1/u du (which is also the same as 3/10 ln(u) Now substitute x back into u Now, rewrite the other part of the integral (complete the square) to find an inverse tan function hidden there. It simplifies to the equation 31/5 (arctan(25x) so the final equation is : 3/10 ln(5x^24x+1) + 31/5 (arctan(25x) +c (do NOT forget the +C after all this work lol)

AnElephant
 2 years ago
Best ResponseYou've already chosen the best response.0if you want a more insightful thought process of a certain part of a problem, please ask (i was kinda just in a hurry to get it done)

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.0woah woah, explain how you rewrote it.. i dont get that..

AnElephant
 2 years ago
Best ResponseYou've already chosen the best response.0Okay, so, we know the derivative of the denominator is 10x4 right? so we just have to do a lot of algebra to get at least one part of the numerator to look like that (its mostly a lucky guess in my case) because i had in the back of my mind that a problem as complex as this needs to use u substitiution

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.0so, i have to get the numerator to be 10x4? (which is the derivative of the denom)

AnElephant
 2 years ago
Best ResponseYou've already chosen the best response.03x+5 = 31/5 + 3/10 (10x4) ; (the 2 numerators of the integrals before i factored out constants

AnElephant
 2 years ago
Best ResponseYou've already chosen the best response.0Yes, in a problem where there is a denominator, you need to first think of substitution and how you can get the derivative of the denominator into the numerator of the function

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.0I still don't get how in the worl you get 31/5+3/10(10x4)... out of 3x+5

AnElephant
 2 years ago
Best ResponseYou've already chosen the best response.0ok, so, we need to get 10x4 out of this so : 3x+5 = 30x+50, then subtract 3(10x4) to get a remainder of 62 (this will go in the 2nd integral)

AnElephant
 2 years ago
Best ResponseYou've already chosen the best response.0keep in mind, this is all over a denominator of 10 (which we inserted into the equation when we multiplied 3x+5 by 10)

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.0so multiply by ten and subtract 3(10x5)?

AnElephant
 2 years ago
Best ResponseYou've already chosen the best response.0yeah, and hope you get lucky later on ; )

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.0how do you subtract 3(10x5) from 30x+50? lol! im so sorry... i just really dont understand

AnElephant
 2 years ago
Best ResponseYou've already chosen the best response.0no problem, ive been told i make a horrible teacher XD (and it's 3(10x4) So, 30x+50  3(10x4) = 30x+50  30x + 12 which makes 62 (the constant in the 2nd integral) then you simply divide by 10 to get 31/5 which is what i factored out of the integral

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.0ahhh, got it,. what you mean constant in the 2nd integral,. ?
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