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Category: Integration

x-6-e-4x-2-dx-

Question Number 117148 by bemath last updated on 10/Oct/20 $$\:\:\:\int\:\mathrm{x}^{\mathrm{6}} \:\mathrm{e}^{−\mathrm{4x}^{\mathrm{2}} } \:\mathrm{dx}\:=? \\ $$ Answered by Olaf last updated on 10/Oct/20 $$ \\ $$$$\mathrm{I}\:=\:\int\left(−\frac{\mathrm{1}}{\mathrm{8}}{x}^{\mathrm{5}}…

nice-mathematics-please-evaluate-x-2-4-x-2-4-sin-2x-x-dx-m-n-1970-

Question Number 117121 by mnjuly1970 last updated on 09/Oct/20 $$\:\:\:\:\:\:\:\:…{nice}\:\:{mathematics}.. \\ $$$$ \\ $$$$\:\:{please}\:\:{evaluate}… \\ $$$$\: \\ $$$$\:\Omega\:=\int_{−\infty} ^{\:+\infty} \left(\frac{{x}^{\mathrm{2}} −\mathrm{4}}{{x}^{\mathrm{2}} +\mathrm{4}}\ast\:\frac{{sin}\left(\mathrm{2}{x}\right)}{{x}}\right)\:{dx}\:=???\:\: \\ $$$$\:{m}.{n}.\mathrm{1970} \\…

0-pi-4-sec-2-x-tan-x-sec-x-dx-

Question Number 182648 by cortano1 last updated on 12/Dec/22 $$\:\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}}{\mathrm{tan}\:\mathrm{x}−\mathrm{sec}\:\mathrm{x}}\:\mathrm{dx}\:=? \\ $$ Answered by Acem last updated on 12/Dec/22 $$\:\mathrm{tan}\:{x}\:−\:\mathrm{sec}\:{x}=\:{t}\:\:…..\:{m} \\ $$$$\:\mathrm{sec}\:{x}\:\left(\mathrm{sec}\:{x}−\:\mathrm{tan}\:{x}\right)\:{dx}=\:{dt}…

sin-6-2x-cos-6-2x-dx-

Question Number 117100 by bemath last updated on 09/Oct/20 $$\int\:\mathrm{sin}\:^{\mathrm{6}} \left(\mathrm{2x}\right)\:\mathrm{cos}\:^{\mathrm{6}} \left(\mathrm{2x}\right)\:\mathrm{dx}\:=? \\ $$ Answered by Dwaipayan Shikari last updated on 09/Oct/20 $$\int\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{6}} }\left({sin}\mathrm{4}{x}\right)^{\mathrm{6}} {dx}…

advanced-calculus-evsluate-I-0-xsin-2x-x-2-4-dx-hint-0-cos-px-x-2-1-dx-pi-2-e-p-p-gt-0-m

Question Number 117088 by mnjuly1970 last updated on 09/Oct/20 $$\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:\:{calculus}… \\ $$$$ \\ $$$$\:\:\:\:\:\:\:{evsluate}\::: \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\mathrm{I}=\int_{\mathrm{0}} ^{\:\infty} \frac{{xsin}\left(\mathrm{2}{x}\right)}{{x}^{\mathrm{2}} +\mathrm{4}}\:{dx}\:=? \\ $$$$\:\:\:\:\:{hint}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\Phi=\int_{\mathrm{0}}…