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Category: Integration

1-calculate-I-n-0-x-n-e-1-i-x-dx-with-n-integr-natural-and-i-2-1-2-find-0-x-4k-3-xsinx-dx-

Question Number 46612 by maxmathsup by imad last updated on 29/Oct/18 $$\left.\mathrm{1}\right)\:{calculate}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:{x}^{{n}} \:{e}^{\left(\mathrm{1}−{i}\right){x}} {dx}\:{with}\:{n}\:{integr}\:{natural}\:{and}\:{i}^{\mathrm{2}} =−\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{\mathrm{0}} ^{\infty} \:{x}^{\mathrm{4}{k}+\mathrm{3}} \:{xsinx}\:{dx}\:. \\ $$…

find-x-x-x-x-dx-

Question Number 46594 by maxmathsup by imad last updated on 29/Oct/18 $${find}\:\int\:\left(\sqrt{{x}+\sqrt{{x}}}−\sqrt{{x}−\sqrt{{x}}}\right){dx} \\ $$ Answered by MJS last updated on 29/Oct/18 $$\int\sqrt{{x}+\sqrt{{x}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{{x}}\:\rightarrow\:{dx}=\mathrm{2}\sqrt{{x}}{dt}\right] \\…

calculus-prove-that-if-0-1-ln-ln-1-x-dx-then-Re-ln-2-m-n-july-1970-

Question Number 112119 by mnjuly1970 last updated on 06/Sep/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:….{calculus}…. \\ $$$${prove}\:{that}::: \\ $$$${if}\:\:\:\Omega\:=\int_{\mathrm{0}\:\:} ^{\:\mathrm{1}} {ln}\left({ln}\left(\mathrm{1}−\sqrt{{x}}\:\right)\right){dx} \\ $$$${then} \\ $$$$\mathscr{R}{e}\left(\Omega\right)\::=\:−\gamma\:+\:{ln}\left(\mathrm{2}\right)…. \\ $$$$ \\ $$$${m}.{n}.\:{july}\:\mathrm{1970}# \\…

using-taylors-expansion-find-find-the-value-of-a-tan45-1-b-sin30-1-

Question Number 46534 by peter frank last updated on 28/Oct/18 $$\mathrm{using}\:\mathrm{taylors}\:\mathrm{expansion} \\ $$$$\mathrm{find}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\left.\mathrm{a}\right)\mathrm{tan45}°\:\mathrm{1}'\: \\ $$$$\left.\mathrm{b}\right)\mathrm{sin30}°\:\mathrm{1}' \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…

Calculate-0-1-ln-x-1-x-2-dx-G-Solution-0-1-k-0-1-k-x-2k-ln-x-dx-k-0-1-k-0-1-x-

Question Number 177604 by mnjuly1970 last updated on 07/Oct/22 $$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{Calculate} \\ $$$$\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\mathrm{ln}\left({x}\:\right)}{\mathrm{1}\:+\:{x}^{\:\mathrm{2}} }\:\mathrm{d}{x}\:\overset{?} {=}\:−\mathrm{G} \\ $$$$\:\:\:\:\sim\:\mathrm{Solution}\:\sim \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \left\{\underset{{k}=\mathrm{0}} {\overset{\infty}…

Question-46499

Question Number 46499 by Tawa1 last updated on 27/Oct/18 Answered by MJS last updated on 27/Oct/18 $$\int\frac{\mathrm{6sin}\:{x}\:\mathrm{cos}^{\mathrm{2}} \:{x}\:+\mathrm{sin}\:\mathrm{2}{x}\:−\mathrm{23sin}\:{x}}{\left(\mathrm{1}−\mathrm{cos}\:{x}\right)^{\mathrm{2}} \left(\mathrm{5}−\mathrm{sin}^{\mathrm{2}} \:{x}\right)}{dx}= \\ $$$$=\int\frac{\mathrm{6cos}^{\mathrm{2}} \:{x}\:+\mathrm{2cos}\:{x}\:−\mathrm{23}}{\left(\mathrm{1}−\mathrm{cos}\:{x}\right)^{\mathrm{2}} \left(\mathrm{4}+\mathrm{cos}^{\mathrm{2}} \:{x}\right)}\mathrm{sin}\:{x}\:{dx}=…

Question-177541

Question Number 177541 by peter frank last updated on 06/Oct/22 Commented by cortano1 last updated on 07/Oct/22 $$\underset{\mathrm{0}} {\overset{\mathrm{k}} {\int}}\:\frac{\mathrm{8}}{\left(\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{3}\right)}\:\mathrm{dx}=\mathrm{ln}\:\mathrm{k}+\frac{\pi\sqrt{\mathrm{3}}}{\mathrm{k}^{\mathrm{2}} }\:? \\ $$ Commented…