Question Number 6248 by FilupSmith last updated on 20/Jun/16 $$\int_{−\infty} ^{\:\infty} {e}^{−{u}} {u}^{{n}} {du}\:=\:??? \\ $$ Commented by 123456 last updated on 20/Jun/16 $$\mathrm{i}\:\mathrm{think}\:\mathrm{that}\:\mathrm{it}\:\mathrm{diverges} \\…
Question Number 6246 by FilupSmith last updated on 20/Jun/16 $$\mathrm{Need}\:\mathrm{help}\:\mathrm{solving}\:\int_{\mathrm{0}} ^{\:\infty} {x}^{−{x}} {dx} \\ $$$$\mathrm{My}\:\mathrm{current}\:\mathrm{working}: \\ $$$${x}^{−{x}} ={e}^{−{x}\mathrm{ln}{x}} \\ $$$${e}^{−{x}\mathrm{ln}{x}} =\mathrm{1}−{x}\mathrm{ln}\left({x}\right)+\frac{{x}^{\mathrm{2}} \mathrm{ln}\left({x}\right)^{\mathrm{2}} }{\mathrm{2}!}−\frac{{x}^{\mathrm{3}} \mathrm{ln}\left({x}\right)^{\mathrm{3}} }{\mathrm{3}!}+……
Question Number 137315 by liberty last updated on 01/Apr/21 $$\int_{\mathrm{0}} ^{\:\pi/\mathrm{4}} \:\sqrt{\mathrm{cos}\:^{\mathrm{3}} \left(\mathrm{2x}\right)}\:\mathrm{dx}\:? \\ $$ Answered by rs4089 last updated on 01/Apr/21 $$\int_{\mathrm{0}} ^{\:\pi/\mathrm{4}} \sqrt{{cos}^{\mathrm{3}}…
Question Number 137307 by mnjuly1970 last updated on 31/Mar/21 $$\:\:\:\:\:\:\:\:…..{advanced}\:\:\:\:{calculus}….. \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{4}{n}^{\mathrm{2}} +\mathrm{1}}\right)=\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{2}+\pi{csch}\left(\frac{\pi}{\mathrm{2}}\right)\right) \\ $$$$\:\:\:\:\:\:………………………. \\ $$ Answered by Dwaipayan…
Question Number 137302 by Eric002 last updated on 31/Mar/21 $$\int\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}}}}}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 6220 by sanusihammed last updated on 18/Jun/16 $$\int\sqrt{{tanx}}\:\:{dx}\: \\ $$ Answered by malwaan last updated on 19/Jun/16 $$\int\sqrt{{tanx}}\:{dx}=\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{2}}}\left(\mathrm{2}{tan}^{−\mathrm{1}} \left(\mathrm{1}+\sqrt{\mathrm{2}{tanx}}\right)\right. \\ $$$$−\mathrm{2}{tan}^{−\mathrm{1}} \left(\mathrm{1}−\sqrt{\mathrm{2}{tanx}}\right) \\…
Question Number 137285 by bemath last updated on 31/Mar/21 $$\int\:\frac{\mathrm{5}+\mathrm{2cos}\:\mathrm{2x}}{\mathrm{4}+\mathrm{2sin}\:\mathrm{2x}}\:\mathrm{dx}\: \\ $$ Answered by EDWIN88 last updated on 31/Mar/21 $$\mathrm{E}=\int\:\frac{\mathrm{2cos}\:\mathrm{2x}}{\mathrm{4}+\mathrm{2sin}\:\mathrm{2x}}\:\mathrm{dx}\:+\:\int\:\frac{\mathrm{5}}{\mathrm{4}+\mathrm{2sin}\:\mathrm{2x}}\:\mathrm{dx} \\ $$$$\mathrm{E}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\int\:\frac{\mathrm{d}\left(\mathrm{4}+\mathrm{2sin}\:\mathrm{2x}\right)}{\mathrm{4}+\mathrm{2sin}\:\mathrm{2x}}\:+\:\int\:\frac{\mathrm{5}}{\mathrm{4}+\mathrm{2sin}\:\mathrm{2x}}\:\mathrm{dx} \\ $$$$\mathrm{E}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\mid\mathrm{4}+\mathrm{2sin}\:\mathrm{2x}\:\mid\:+\:\int\:\frac{\mathrm{5}}{\mathrm{4}+\mathrm{2sin}\:\mathrm{2x}}\:\mathrm{dx}\: \\…
Question Number 6214 by sanusihammed last updated on 18/Jun/16 $$\int\sqrt{{tanx}}\:\:{dx}\: \\ $$ Commented by nburiburu last updated on 24/Jun/16 $${by}\:\:{substitution} \\ $$$${t}=\sqrt{{tan}\:{x}}\Rightarrow{t}^{\mathrm{2}} =\:{tan}\:{x} \\ $$$$\mathrm{2}{t}\:{dt}\:=\:{sec}^{\mathrm{2}}…
Question Number 137277 by mnjuly1970 last updated on 31/Mar/21 $$ \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {sin}^{\mathrm{2}} \left({x}\right).{ln}\left({sin}\left({x}\right)\right){dx}=? \\ $$$$ \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 6205 by sanusihammed last updated on 18/Jun/16 $${Show}\:{that} \\ $$$$\int_{\mathrm{42}} ^{\mathrm{7}} \:\left(\mathrm{4}{x}\:−\:\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} \:{dx}\:\:=\:\:\mathrm{15} \\ $$ Answered by FilupSmith last updated on 18/Jun/16 $$\int_{\mathrm{42}}…