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Category: Integration

3x-2-1-x-4-1-dx-

Question Number 130778 by EDWIN88 last updated on 28/Jan/21 $$\int\:\frac{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{4}} −\mathrm{1}}\:{dx}\: \\ $$ Answered by bemath last updated on 29/Jan/21 $$\:\frac{\mathrm{3x}^{\mathrm{2}} −\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)}\:=\:\frac{\mathrm{3}\left(\mathrm{x}^{\mathrm{2}}…

Question-65200

Question Number 65200 by rajesh4661kumar@gmail.com last updated on 26/Jul/19 Answered by ajfour last updated on 26/Jul/19 $${I}=\int\sqrt{\mathrm{tan}\:{x}}{dx} \\ $$$${let}\:\mathrm{tan}\:{x}={t}^{\mathrm{2}} \:\Rightarrow\:{dx}=\frac{\mathrm{2}{tdt}}{\mathrm{1}+{t}^{\mathrm{2}} } \\ $$$$\Rightarrow\:{I}=\int\frac{\mathrm{2}{t}^{\mathrm{2}} {dt}}{\mathrm{1}+{t}^{\mathrm{4}} }…