(adsbygoogle = window.adsbygoogle || []).push({}); 1. Problem with Integral

I got stuck on the following Integal and can't find the mistake:

[tex]Integral(x/(x-1))[/tex]

let U' = x and V = (x-1)^(-1)

and U= 0.5x^2 V' = 1/(x-1)^2

so: [tex]x^2/(2(x-1))-1/2Integral(x^2/(x-1)^2[/tex]

algebraic division: [tex]x^2 : (x^2 -2x + 1) = 1- 1/(x-1)^2 + 1/(x-1)^2[/tex]

substituting back into equation gives:

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

but the result is supposed to be:

[tex]x + ln(x-1)[/tex]

2. Substitution in ODE

[tex]xydy/dx + (x^2 + y^2 +x) = 0 [/tex]

I have tried to substitute z = xy and also z = x^2 + y^2, but that didn't work. Any other ideas?

Thank you!

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# Homework Help: Integral and ODE

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