GregA
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A pretty simple question that is doing my head in is the folllowing:
Integrate (x+1)/x(2x+1) w.r.t.x
by choosing to use partial fractions of the form A/x + B/2x+1 my working is as follows:
using the cover up method and x = 0 to find A I get A =1 ...(0+1)/(2(0)+1)
using x = -1/2 to find B I get B = -1...((-1/2+1)/-1/2)
this leaves me with 1/x - 1/(2x+1) to be integrated.
my answer being lnA + lnx +1/2ln(2x+1) or lnA(x/((2x+1)^(1/2)) (because 1 is half the derivative of 2x)...the books answer is simply ln(x/2x+1)...they omit the constant by specifying that all answers should include it...My question is: is there something wrong with my working or is the book's answer wrong and I should move on?
Integrate (x+1)/x(2x+1) w.r.t.x
by choosing to use partial fractions of the form A/x + B/2x+1 my working is as follows:
using the cover up method and x = 0 to find A I get A =1 ...(0+1)/(2(0)+1)
using x = -1/2 to find B I get B = -1...((-1/2+1)/-1/2)
this leaves me with 1/x - 1/(2x+1) to be integrated.
my answer being lnA + lnx +1/2ln(2x+1) or lnA(x/((2x+1)^(1/2)) (because 1 is half the derivative of 2x)...the books answer is simply ln(x/2x+1)...they omit the constant by specifying that all answers should include it...My question is: is there something wrong with my working or is the book's answer wrong and I should move on?
