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I have to find the integral of [tex](4-x)x^{-3}[/tex]. My TI-89 says it should be [tex]\frac{x-2}{x^{2}}+C[/tex] but I can't seem to get it myself.

I rearranged it to get [tex](4x^{-1}-1)x^{-2}[/tex] and then I used U-Substitution. And set [tex]U = 4x^{-1}-1[/tex] so that [tex]dU = -4x^{-2}dx[/tex]Then I rewrote the integral as [tex]-\frac{1}{4}\int Udu[/tex] and evaluated it to get [tex]-\frac{1}{8}U^{2}+C[/tex]or [tex]-\frac{1}{8}(4x^{-1}-1)^{2}+C[/tex] which works out to [tex]-\frac{(x-4)^{2}}{8x^{2}}+C[/tex]which is not what my calculator says it should be.

What am I doing wrong?

...and if I have to make another Latex equation...

I rearranged it to get [tex](4x^{-1}-1)x^{-2}[/tex] and then I used U-Substitution. And set [tex]U = 4x^{-1}-1[/tex] so that [tex]dU = -4x^{-2}dx[/tex]Then I rewrote the integral as [tex]-\frac{1}{4}\int Udu[/tex] and evaluated it to get [tex]-\frac{1}{8}U^{2}+C[/tex]or [tex]-\frac{1}{8}(4x^{-1}-1)^{2}+C[/tex] which works out to [tex]-\frac{(x-4)^{2}}{8x^{2}}+C[/tex]which is not what my calculator says it should be.

What am I doing wrong?

...and if I have to make another Latex equation...

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