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x-2-1-ln-x-2-1-2lnx-x-4-dx-

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Question Number 335 by Vishal Bhardwaj last updated on 22/Dec/14
∫ (((√((x^2 +1)))[ln(x^2 +1)−2lnx])/x^4 ) dx
$$\int\:\frac{\sqrt{\left({x}^{\mathrm{2}} +\mathrm{1}\right)}\left[{ln}\left({x}^{\mathrm{2}} +\mathrm{1}\right)−\mathrm{2}{lnx}\right]}{{x}^{\mathrm{4}} }\:{dx} \\ $$
Commented by 123456 last updated on 22/Dec/14
((√(x^2 +1))/x^4 )ln ((x^2 +1)/x^2 )
$$\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}{{x}^{\mathrm{4}} }\mathrm{ln}\:\frac{{x}^{\mathrm{2}} +\mathrm{1}}{{x}^{\mathrm{2}} } \\ $$
Commented by 123456 last updated on 23/Dec/14
(((x^2 +1)^(3/2) [−3ln(x^2 +1)+6ln x+2])/(9x^3 ))
$$\frac{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}/\mathrm{2}} \left[−\mathrm{3ln}\left({x}^{\mathrm{2}} +\mathrm{1}\right)+\mathrm{6ln}\:{x}+\mathrm{2}\right]}{\mathrm{9}{x}^{\mathrm{3}} } \\ $$

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