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Category: Integration

Question-178246

Question Number 178246 by mnjuly1970 last updated on 14/Oct/22 Answered by CElcedricjunior last updated on 14/Oct/22 $$\boldsymbol{\Omega}=\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{\mathrm{ln}}^{\mathrm{2}} \left(\boldsymbol{\mathrm{x}}\right)}{\mathrm{1}+\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\boldsymbol{\mathrm{dx}}=\frac{\boldsymbol{\pi}}{\mathrm{64}}\left(\boldsymbol{{a}\zeta}\left(\mathrm{2}\right)+{b}\boldsymbol{\mathrm{ln}}^{\mathrm{2}} \left(\mathrm{2}\right)\right) \\ $$$$\boldsymbol{\Omega}=\int_{\mathrm{0}} ^{\infty}…

1-sin-x-e-cos-x-cos-x-dx-2-1-1-sin-2A-1-1-sin-2A-3-dx-x-b-x-2-a-2-

Question Number 112699 by bemath last updated on 09/Sep/20 $$\:\left(\mathrm{1}\right)\:\int\:\frac{\mathrm{sin}\:\mathrm{x}\:\mathrm{e}^{\sqrt{\mathrm{cos}\:\mathrm{x}}} }{\:\sqrt{\mathrm{cos}\:\mathrm{x}}}\:\mathrm{dx}\: \\ $$$$\:\left(\mathrm{2}\right)\:\frac{\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{2A}}}{\mathrm{1}−\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{2A}}}??\: \\ $$$$\left(\mathrm{3}\right)\int\:\frac{\mathrm{dx}}{\left(\mathrm{x}+\mathrm{b}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{a}^{\mathrm{2}} \right)} \\ $$ Commented by Dwaipayan Shikari last updated…

tan-1-1-x-x-1-dx-

Question Number 112666 by bemath last updated on 09/Sep/20 $$\int\:\mathrm{tan}^{−\mathrm{1}} \left(\sqrt{\frac{\mathrm{1}−\mathrm{x}}{\mathrm{x}+\mathrm{1}}}\right)\:\mathrm{dx}\:? \\ $$ Answered by Her_Majesty last updated on 09/Sep/20 $${by}\:{parts} \\ $$$${u}'=\mathrm{1}\:\Rightarrow\:{u}={x} \\ $$$${v}={tan}^{−\mathrm{1}}…