Question Number 8763 by tawakalitu last updated on 26/Oct/16 $$\int\mathrm{x}\sqrt{\mathrm{3x}\:+\:\mathrm{1}}\:\:\mathrm{dx} \\ $$ Commented by FilupSmith last updated on 26/Oct/16 $${u}=\mathrm{3}{x}+\mathrm{2}\Rightarrow{x}=\frac{\mathrm{1}}{\mathrm{3}}\left({u}−\mathrm{2}\right) \\ $$$${du}=\mathrm{3}{dx} \\ $$$$\frac{\mathrm{1}}{\mathrm{3}}\int\mathrm{3}{x}\sqrt{\mathrm{3}{x}+\mathrm{2}}{dx} \\…
Question Number 139826 by qaz last updated on 01/May/21 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\:\left[\left({n}−\mathrm{1}\right){x}\right]}{\mathrm{4}^{{n}+\mathrm{1}} }=? \\ $$ Answered by mnjuly1970 last updated on 01/May/21 $$\:\:\:\:\:\Omega:=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{sin}\left(\left({n}−\mathrm{1}\right){x}\right)}{\mathrm{4}^{{n}+\mathrm{1}}…
Question Number 139811 by mnjuly1970 last updated on 01/May/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}:=\int_{\mathrm{0}} ^{\:\mathrm{1}} \sqrt{{x}}\:{ln}\left(\frac{\mathrm{1}}{\mathrm{1}−{x}}\right){dx} \\ $$$$\:\:\:\:\:{solution}: \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\phi}:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \sqrt{{x}}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{x}^{{n}} }{{n}}\:{dx} \\ $$$$\:\:\:\:\:\:\:\:\::=\underset{{n}=\mathrm{1}}…
Question Number 8734 by tawakalitu last updated on 24/Oct/16 $$\mathrm{Evaluate}\:\mathrm{the}\:\mathrm{integral} \\ $$$$\int\left[\mathrm{a}\left(\overset{\bullet} {\mathrm{b}}.\mathrm{a}\:+\:\mathrm{b}.\overset{\bullet} {\mathrm{a}}\right)\:+\:\overset{\bullet} {\mathrm{a}}\left(\mathrm{b}.\mathrm{a}\right)\:−\:\mathrm{2}\left(\overset{\bullet} {\mathrm{a}}.\mathrm{a}\right)\mathrm{b}\:−\:\overset{\bullet} {\mathrm{b}}\mid\mathrm{a}\mid^{\mathrm{2}} \right]\mathrm{dt} \\ $$$$\mathrm{In}\:\mathrm{which}\:\:\overset{\bullet} {\mathrm{a}}\:,\overset{\bullet} {\mathrm{b}}\:\:\mathrm{are}\:\mathrm{the}\:\mathrm{derivatives}\:\mathrm{of}\:\:\mathrm{a},\mathrm{b}\:\mathrm{with}\: \\ $$$$\mathrm{respect}\:\mathrm{to}\:\mathrm{t} \\…
Question Number 74264 by malikmasood3535@gmail.com last updated on 21/Nov/19 $$\int_{\mathrm{0}} ^{{x}} {xe}^{{x}} \mathrm{sin}\:{e}^{{x}} {e}^{{x}} {dx} \\ $$ Commented by MJS last updated on 21/Nov/19 $$\left(\mathrm{1}\right)\:\mathrm{dependent}\:\mathrm{borders}\:\mathrm{error}…
Question Number 8728 by kuldeep singh raj last updated on 24/Oct/16 $$\int\mathrm{cos}\:{x}/\mathrm{4}−{x}^{\mathrm{2}} \\ $$$$\int\frac{\mathrm{cos}\:{x}}{\mathrm{4}−{x}^{\mathrm{2}} } \\ $$$$ \\ $$ Commented by prakash jain last updated…
Question Number 74263 by malikmasood3535@gmail.com last updated on 21/Nov/19 $$\int_{\mathrm{0}} ^{{x}} {e}^{{x}} \mathrm{cos}\:{e}^{{x}} {e}^{{x}} {dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 139789 by mnjuly1970 last updated on 01/May/21 $$\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:……\mathscr{M}{athematical}\:…\:…\:…\:\mathscr{A}{nalysis}……. \\ $$$$\:\:\:\:{evaluation}\:::\:\mathscr{F}\::=\int_{\mathrm{0}} ^{\:\infty} {e}^{\frac{−\mathrm{2}}{{x}}} {sin}^{\mathrm{2}} \left(\frac{\mathrm{2}}{{x}}\right){dx}=? \\ $$$$ \\ $$$$\:\:\:\: \\ $$ Answered…
Question Number 74231 by necxxx last updated on 20/Nov/19 Commented by necxxx last updated on 20/Nov/19 Commented by necxxx last updated on 20/Nov/19 $${here}\:{was}\:{a}\:{step}\:{taken}\:{though}\:{not}\:{so} \\…
Question Number 74224 by mathmax by abdo last updated on 20/Nov/19 $${find}\:\int\:\:\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} \:{cos}\left(\frac{\mathrm{1}}{\mathrm{2}}{arctan}\left(\frac{\mathrm{1}}{{x}}\right)\right){dx}\:\:{and} \\ $$$$\int\:\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} {sin}\left(\frac{\mathrm{1}}{\mathrm{2}}{arctan}\left(\frac{\mathrm{1}}{{x}}\right)\right){dx} \\ $$ Commented by mathmax by abdo…