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Category: Integration

Question-156182

Question Number 156182 by cortano last updated on 09/Oct/21 Answered by PRITHWISH SEN 2 last updated on 10/Oct/21 $$\int\frac{\mathrm{sec}^{\mathrm{4}} \mathrm{xdx}}{\mathrm{12tan}\:^{\mathrm{2}} \mathrm{x}−\mathrm{4}}\:=\:\int\frac{\mathrm{sec}^{\mathrm{2}} \mathrm{x}\left(\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}\right)\mathrm{dx}}{\mathrm{12tan}\:^{\mathrm{2}} \mathrm{x}−\mathrm{4}} \\…

1-x-x-2-x-1-dx-

Question Number 90589 by M±th+et£s last updated on 24/Apr/20 $$\int\frac{\mathrm{1}}{{x}+\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}{dx} \\ $$ Commented by mathmax by abdo last updated on 24/Apr/20 $${I}\:=\int\:\:\frac{{dx}}{{x}+\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}\:=\int\:\:\frac{{dx}}{{x}+\sqrt{\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} +\frac{\mathrm{3}}{\mathrm{4}}}}…

Use-gamma-function-to-prove-i-0-8-cos-3-4x-dx-1-6-ii-0-6-cos-4-3-sin-2-6-d-5-192-

Question Number 90574 by niroj last updated on 24/Apr/20 $$\:\boldsymbol{\mathrm{Use}}\:\boldsymbol{\mathrm{gamma}}\:\boldsymbol{\mathrm{function}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{prove}} \\ $$$$\:\:\left(\mathrm{i}\right)\:.\:\:\int_{\mathrm{0}} ^{\:\:\frac{\boldsymbol{\pi}}{\mathrm{8}}} \:\boldsymbol{\mathrm{cos}}^{\mathrm{3}} \mathrm{4}\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{dx}}=\:\frac{\mathrm{1}}{\mathrm{6}}. \\ $$$$\:\:\left(\boldsymbol{\mathrm{ii}}\right).\:\int_{\mathrm{0}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{6}}} \:\boldsymbol{\mathrm{cos}}^{\mathrm{4}} \mathrm{3}\boldsymbol{\theta}\:\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \mathrm{6}\boldsymbol{\theta}\:\boldsymbol{\mathrm{d}\theta}\:=\:\frac{\mathrm{5}\boldsymbol{\pi}}{\mathrm{192}}. \\ $$ Commented by…

dx-2-cos-x-

Question Number 90544 by jagoll last updated on 24/Apr/20 $$\int\:\frac{{dx}}{\:\sqrt{\mathrm{2}−\mathrm{cos}\:{x}}} \\ $$ Answered by $@ty@m123 last updated on 24/Apr/20 $$\int\frac{{dx}}{\:\sqrt{\mathrm{2}−\frac{\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}}} \\ $$$$\int\frac{{dx}}{\:\sqrt{\frac{\mathrm{2}+\mathrm{2tan}\:^{\mathrm{2}} \frac{{x}}{\mathrm{2}}+\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}}…