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Category: Integration

advanced-integral-prove-that-0-sin-2-x-x-2-1-x-2-dx-pi-4-1-pi-e-2-

Question Number 123900 by mnjuly1970 last updated on 29/Nov/20 $$\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:{integral}… \\ $$$$\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}^{\mathrm{2}} \left({x}\right)}{{x}^{\mathrm{2}} \left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{dx}\:=\frac{\pi}{\mathrm{4}}\left(\mathrm{1}+\frac{\pi}{{e}^{\mathrm{2}} }\right) \\ $$ Answered by mathmax…

0-pi-sin-2-x-x-dx-

Question Number 123896 by john_santu last updated on 29/Nov/20 $$\:\:\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{\mathrm{sin}\:^{\mathrm{2}} {x}}{\:\sqrt{{x}}}\:{dx} \\ $$ Answered by mindispower last updated on 29/Nov/20 $${sin}^{\mathrm{2}} \left({x}\right)=\frac{\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}} \\…

To-mr-mjs-sir-integral-lover-0-pi-4-tan-pi-4-x-cos-2-x-tan-3-x-tan-2-x-tan-x-dx-

Question Number 123866 by benjo_mathlover last updated on 28/Nov/20 $$\:{To}\:{mr}\:{mjs}\:{sir}.\: \\ $$$${integral}\:{lover}\: \\ $$$$\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\frac{\mathrm{tan}\:\left(\frac{\pi}{\mathrm{4}}−{x}\right)}{\mathrm{cos}\:^{\mathrm{2}} {x}\:\sqrt{\mathrm{tan}\:^{\mathrm{3}} {x}+\mathrm{tan}\:^{\mathrm{2}} {x}+\mathrm{tan}\:{x}}}\:{dx}\:=?\: \\ $$ Answered by liberty last…

sect-e-t-dt-

Question Number 123859 by sdfg last updated on 28/Nov/20 $$\int{sect}\:{e}^{{t}} \:{dt} \\ $$ Answered by mindispower last updated on 29/Nov/20 $${sec}\left({x}\right)=\frac{\mathrm{2}}{{e}^{{ix}} +{e}^{−{ix}} },{we}\:{use}\:{cos}\left({x}\right)=\frac{{e}^{{ix}} +{e}^{−{ix}} }{\mathrm{2}}…

a-dx-2sin-2-x-3tg-2-x-b-1-x-1-3-1-x-x-1-3-x-1-6-dx-c-cosx-1-cos2x-dx-d-sin-2-x-2-3-cos-2-x-dx-

Question Number 58259 by behi83417@gmail.com last updated on 20/Apr/19 $$\boldsymbol{\mathrm{a}}\:\:.\int\:\:\frac{\boldsymbol{\mathrm{dx}}}{\mathrm{2}\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}+\mathrm{3}\boldsymbol{\mathrm{tg}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}}=? \\ $$$$\boldsymbol{\mathrm{b}}\:\:\:.\int\frac{\:\:\mathrm{1}+\sqrt[{\mathrm{3}}]{\boldsymbol{\mathrm{x}}}}{\mathrm{1}+\sqrt{\boldsymbol{\mathrm{x}}}+\sqrt[{\mathrm{3}}]{\boldsymbol{\mathrm{x}}}+\sqrt[{\mathrm{6}}]{\boldsymbol{\mathrm{x}}}}\boldsymbol{\mathrm{dx}}=? \\ $$$$\boldsymbol{\mathrm{c}}\:\:\:\:\:.\int\:\:\frac{\boldsymbol{\mathrm{cosx}}}{\mathrm{1}+\boldsymbol{\mathrm{cos}}\mathrm{2}\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{dx}}=? \\ $$$$\boldsymbol{\mathrm{d}}\:\:\:\:\:.\int\:\:\:\frac{\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}}{\:\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}.\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{dx}}=? \\ $$ Commented by maxmathsup…