- #1

jessjolt

- 3

- 0

My attempt:

(arctan x) / ((x+1)(x^2+1)) = A/(x+1) + (Bx+C)/(x^2+1)

arctan x = A(x^2+1) + (Bx+C)(x+1)

when x= -1, A= -pi/8

so plugging in -pi/8 for B makes:

x= tan[ (B-(pi/8))x^2 + (B+C)x + (C-(pi/8)) ]

and when x=0, C= pi/8

so plugging in pi/8 for C and rearranging produces:

x=tan[ B(x^2+x) + (((pi*x)/8)*(1-x)) ]

and when x=1, B=pi/8

so (arctan x) / ((x+1)(x^2+1)) = [(-pi/8)/(x+1)] + {{ [(pi*x)/8] + (pi/8) }/(x^2+1) }

but when i graph in radian mode on a graphic calculator (arctan x) / ((x+1)(x^2+1)) and my result, they are not the same thing, so my answer must be wrong. The graphs appear very similar though, so it seems there is only a small error? Please help?? :D