integrate 2 / x(x^2+1)^2

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integrate 2 / x(x^2+1)^2

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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try substitution t=x^2 dt=2xdx 1/2dt=xdx
can i do partial fraction method?
\[\int\limits \frac{ 2 }{ x (x^2+1)^2} dx\] Hmm. Use partial fractions?

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yes you can use partial fraction . i guess fractions will be easy with linear terms so use t=x^2 dt=2xdx \[\Large \int\limits \frac{dt}{t(t+1)^2}\] now use partial fractions .
no we can write the original integral as \[\Large \int\limits \frac{2xdx}{x^2(x^2+1)}\] so let t=x^2 dt=2xdx
\[2\left( \frac{ 1 }{ 2(x^2+1) }-\frac{ 1 }{ 2 }\log(x^2+1)+\log x \right)\]
@sami-21 i dont understand
you can use partial fraction, this is because if the power of the denominator is greater than the power of the numerator that would be an alternative method...
but for me personal i prefer the first method present by sami....
okay thank you!
you're welcome
did u solve the problem?

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