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Evaluate the Integral:

[tex] \int \frac {2x+1}{(x^{2}+9)^{2}}[/tex]

My attempt:

[tex] \frac {2x+1}{(x^{2}+9)^{2}} = \frac {Ax+B}{x^{2}+9} + \frac {Cx+D}{(x^{2} + 9)^{2}}[/tex]

= [tex] (Ax+B)(x^{2} + 9)^{2} + (Cx+D)(x^{2} + 9) [/tex]

= [tex] Ax^{5} + Bx^{4} Dx^{3} + (18A + E)x^{2} + (81A+9D+18B)x + 9E + 81B[/tex]

I'm not sure what I'm doing wrong here since I can't find value of A B C or D.

2nd attempt:

[tex] \frac {2x+1}{(x^{2}+9)^{2}} = \frac {Ax+B}{x^{2}+9} + \frac {Cx+D}{(x^{2} + 9)^{2}}[/tex]

[tex] 2x + 1 = (Ax+B)(x^{2}+9) + Cx + D [/tex]

Still not sure what I'm doing wrong.

[tex] \int \frac {2x+1}{(x^{2}+9)^{2}}[/tex]

My attempt:

[tex] \frac {2x+1}{(x^{2}+9)^{2}} = \frac {Ax+B}{x^{2}+9} + \frac {Cx+D}{(x^{2} + 9)^{2}}[/tex]

= [tex] (Ax+B)(x^{2} + 9)^{2} + (Cx+D)(x^{2} + 9) [/tex]

= [tex] Ax^{5} + Bx^{4} Dx^{3} + (18A + E)x^{2} + (81A+9D+18B)x + 9E + 81B[/tex]

I'm not sure what I'm doing wrong here since I can't find value of A B C or D.

2nd attempt:

[tex] \frac {2x+1}{(x^{2}+9)^{2}} = \frac {Ax+B}{x^{2}+9} + \frac {Cx+D}{(x^{2} + 9)^{2}}[/tex]

[tex] 2x + 1 = (Ax+B)(x^{2}+9) + Cx + D [/tex]

Still not sure what I'm doing wrong.

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