Question

Need help solving this integral using partial fraction decompostion.

Answer 1

The problem is?

Answer 2

\[\int\limits_{}^{}\frac{ y ^{2}+2y+1 }{ (y ^{2} + 1)^{2} } dx\]

Answer 3

I break it down into (Ay+B)/ (y^2+1) + (Cy+D)/ (y^2+1) ^2

Answer 4

\[\frac{ Ax+B }{(y^2+1) } + \frac{ Cx+D }{ (y^2+1)^2 }\]

Answer 5

Where I get stuck is when I go back and find my system of equations. Somehow I get

C=0
A+2C = 0
A+C =2

Answer 6

Yes, I have that Algebraic.

Answer 7

actually not much need of that,,
numerator is (y^2 +1) + 2y
convert it into 2 different integrals
i.e
(y^2 +1)/(y^2 +1)^2 + 2y/(y^2 + 1)

integrate them separately,
1st one shall give tan^-1 y
and in 2nd one, numerator is differential of denominator,,
hope it helps..

Answer 8

yep so
Cy^3 +Dy^2 +Cy +D +Ax+B =y^2 +2y +1

Answer 9

correction --> its 2y/(y^2 +1)^2
and not 2y/(y^2 +1)

Answer 10

I found my mistake...... I multiplied Ay+B by y^2+1

and I multiplied Cy+D by y^2+1)^2

Answer 11

Awesome. Thanks guys.

Answer 12

I was wondering why I had about 7 equations in my system