[tex]\frac{xy'}{(\ln x\arctan y)-1}=(1+y^2)\arctan y\\[/tex](adsbygoogle = window.adsbygoogle || []).push({});

[tex]t=\arctan y\\[/tex]

[tex]t'=\frac{1}{1+y^2}y'\\[/tex]

[tex]\frac{x}{\ln (x)t-1}=\frac{t}{t'}\\[/tex]

[tex]\frac{x}{\ln (x)t-1}=\frac{tdx}{dt}\\[/tex]

[tex]xdt=(\ln (x)t-1)tdx\\[/tex]

[tex]\frac{dt}{\ln (x)t-1}=\frac{dx}{x}\\[/tex]

still cant beak it as one type of variable on each side

so i substitute by another variable

[tex]z=\ln x\\[/tex]

[tex]dz=\frac{dx}{x}\\[/tex]

[tex]\frac{dt}{zt-1}=dz\\[/tex]

i dont know how to separate each variable type on one side

so i could integrate

??

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# Variable substitution question(diff)

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