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Question-124903




Question Number 124903 by Algoritm last updated on 06/Dec/20
Answered by MJS_new last updated on 06/Dec/20
just decompose and solve, no special  knowledge necessary. the answer is:  ((x−1)/(2(x^2 +1)))+(1/4)ln (x^2 +1) −(1/2)ln ∣x+1∣ +C  now try to reach this for yourself
$$\mathrm{just}\:\mathrm{decompose}\:\mathrm{and}\:\mathrm{solve},\:\mathrm{no}\:\mathrm{special} \\ $$$$\mathrm{knowledge}\:\mathrm{necessary}.\:\mathrm{the}\:\mathrm{answer}\:\mathrm{is}: \\ $$$$\frac{{x}−\mathrm{1}}{\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}+\frac{\mathrm{1}}{\mathrm{4}}\mathrm{ln}\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)\:−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\mid{x}+\mathrm{1}\mid\:+{C} \\ $$$$\mathrm{now}\:\mathrm{try}\:\mathrm{to}\:\mathrm{reach}\:\mathrm{this}\:\mathrm{for}\:\mathrm{yourself} \\ $$
Commented by $@y@m last updated on 07/Dec/20
I liked your approach. I think all of us should give hint instead of spoon feeding by solving problems step wise.
Commented by MJS_new last updated on 07/Dec/20
some people here tend to let us do their  homework. others seem to never learn  anything, posting similar questions again  and again... and yet others search the web  for hard looking problems, particularly with  terrifically huge numbers...
$$\mathrm{some}\:\mathrm{people}\:\mathrm{here}\:\mathrm{tend}\:\mathrm{to}\:\mathrm{let}\:\mathrm{us}\:\mathrm{do}\:\mathrm{their} \\ $$$$\mathrm{homework}.\:\mathrm{others}\:\mathrm{seem}\:\mathrm{to}\:\mathrm{never}\:\mathrm{learn} \\ $$$$\mathrm{anything},\:\mathrm{posting}\:\mathrm{similar}\:\mathrm{questions}\:\mathrm{again} \\ $$$$\mathrm{and}\:\mathrm{again}…\:\mathrm{and}\:\mathrm{yet}\:\mathrm{others}\:\mathrm{search}\:\mathrm{the}\:\mathrm{web} \\ $$$$\mathrm{for}\:\mathrm{hard}\:\mathrm{looking}\:\mathrm{problems},\:\mathrm{particularly}\:\mathrm{with} \\ $$$$\mathrm{terrifically}\:\mathrm{huge}\:\mathrm{numbers}… \\ $$

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