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Question Number 27083 by hp killer last updated on 01/Jan/18

∫3x^2 /x^6 +1

$$\int\mathrm{3}{x}^{\mathrm{2}} /{x}^{\mathrm{6}} +\mathrm{1} \\ $$$$ \\ $$

Answered by mrW1 last updated on 01/Jan/18

∫((3x^2 )/(x^6 +1))dx  =∫(1/((x^3 )^2 +1))dx^3   =tan^(−1) x^3 +C

$$\int\frac{\mathrm{3}{x}^{\mathrm{2}} }{{x}^{\mathrm{6}} +\mathrm{1}}{dx} \\ $$$$=\int\frac{\mathrm{1}}{\left({x}^{\mathrm{3}} \right)^{\mathrm{2}} +\mathrm{1}}{dx}^{\mathrm{3}} \\ $$$$=\mathrm{tan}^{−\mathrm{1}} {x}^{\mathrm{3}} +{C} \\ $$

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