Integral of (x^3+x+2)/(x^4 +2x^2 +1) using Partial Fractions
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Integral of (x^3+x+2)/(x^4 +2x^2 +1) using Partial Fractions

[From: ] [author: ] [Date: 12-05-03] [Hit: ]
x) =1/2 ln(x^2+1) + arctan(x) + x / [1 + x^2] + CThere were several smaller steps Ive excluded in the above calculation, if you need help or clarifications please post a comment and Ill address them. I hope this helps.-=[(x^3+1)+x+1]/(x^2+1)^2=[(x+1)(x^2-x+1)+(x+1)]/(x^2+1)^2=(x+1)(x^2-x+2)/(x^2+1)^2there seems something wrong with the question.......
So, we have
int(2 sec^2 (v) dv / [ (tan^2 (v) + 1)^2 ], v) = 2 int( dv/sec^2 (v), v)
= 2 int( cos^2 (v), v)
= int( 1 + cos(2v), v)
= v + 1/2 * sin(2v) + C
= arctan(x) + x / [1 + x^2] + C
Putting these two together, we have
int( [ x^3 + x + 2] / [ x^4 + 2 x^2 + 1] dx, x) = 1/2 ln(x^2+1) + arctan(x) + x / [1 + x^2] + C
There were several smaller steps I've excluded in the above calculation, if you need help or clarifications please post a comment and I'll address them. I hope this helps.

-
=[(x^3+1)+x+1]/(x^2+1)^2
=[(x+1)(x^2-x+1)+(x+1)]/(x^2+1)^2
=(x+1)(x^2-x+2)/(x^2+1)^2

there seems something wrong with the question. sorry
keywords: Fractions,Integral,using,Partial,of,Integral of (x^3+x+2)/(x^4 +2x^2 +1) using Partial Fractions
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