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Category: Integration

Question-176991

Question Number 176991 by mathlove last updated on 29/Sep/22 Answered by som(math1967) last updated on 29/Sep/22 $$\int\frac{{dx}}{{x}^{\mathrm{4}} +\mathrm{8}{x}^{\mathrm{2}} +\mathrm{16}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{8}}\int\frac{\mathrm{8}{dx}}{{x}^{\mathrm{4}} +\mathrm{8}{x}^{\mathrm{2}} +\mathrm{16}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{8}}\int\frac{\frac{\mathrm{8}}{{x}^{\mathrm{2}}…

please-evaluate-I-0-pi-2-1-ln-tan-x-1-1-tan-x-dx-M-N-july-1970-

Question Number 111429 by mnjuly1970 last updated on 03/Sep/20 $$\:\:\:\:\:\:{please}\:\:{evaluate}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:….\:\:\mathrm{I}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \left(\frac{\mathrm{1}}{{ln}\left({tan}\left({x}\right)\right)}\:+\:\frac{\mathrm{1}}{\mathrm{1}−{tan}\left({x}\right)}\right){dx}\:=??? \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\::::\:\:\:\:\mathscr{M}.\:\mathscr{N}.{july}\:\mathrm{1970}\:::: \\ $$$$\:\: \\ $$ Answered…

Question-45885

Question Number 45885 by Meritguide1234 last updated on 17/Oct/18 Commented by maxmathsup by imad last updated on 18/Oct/18 $${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{n}\left(\mathrm{1}−\left({sinx}\right)^{\frac{\mathrm{1}}{{n}}} \right){dx}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:{f}_{{n}}…

some-practice-for-the-brave-cos-2-x-sin-2-x-cos-x-sin-x-dx-cos-2-x-tan-2-x-cos-x-tan-x-dx-sin-2-x-tan-2-x-sin-x-tan-x-dx-

Question Number 45802 by MJS last updated on 17/Oct/18 $$\mathrm{some}\:\mathrm{practice}\:\mathrm{for}\:\mathrm{the}\:\mathrm{brave}… \\ $$$$\int\frac{\mathrm{cos}^{\mathrm{2}} \:{x}\:\mathrm{sin}^{\mathrm{2}} \:{x}}{\mathrm{cos}\:{x}\:+\mathrm{sin}\:{x}}{dx}=? \\ $$$$\int\frac{\mathrm{cos}^{\mathrm{2}} \:{x}\:\mathrm{tan}^{\mathrm{2}} \:{x}}{\mathrm{cos}\:{x}\:+\mathrm{tan}\:{x}}{dx}=? \\ $$$$\int\frac{\mathrm{sin}^{\mathrm{2}} \:{x}\:\mathrm{tan}^{\mathrm{2}} \:{x}}{\mathrm{sin}\:{x}\:+\mathrm{tan}\:{x}}{dx}=? \\ $$ Commented…

find-dx-cosx-sin-2-x-

Question Number 45795 by maxmathsup by imad last updated on 16/Oct/18 $${find}\:\int\:\frac{{dx}}{{cosx}\:{sin}^{\mathrm{2}} {x}} \\ $$ Answered by MJS last updated on 17/Oct/18 $$\frac{\mathrm{1}}{\mathrm{cos}\:{x}\:\mathrm{sin}^{\mathrm{2}} \:{x}}=\left(\mathrm{1}+\frac{\mathrm{cos}^{\mathrm{2}} \:{x}}{\mathrm{sin}^{\mathrm{2}}…