Question Number 153949 by talminator2856791 last updated on 12/Sep/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{sin}\left({x}^{\mathrm{2}} \right)\mathrm{cos}\left({x}^{\mathrm{3}} \right){dx} \\ $$$$\: \\ $$ Answered by mindispower last updated…
Question Number 88415 by abdomathmax last updated on 10/Apr/20 $${find}\:{L}\left(\frac{\mathrm{1}−{cosx}}{{x}^{\mathrm{2}} }\right)\:{with}\:{L}\:{lsplace}\:{transform} \\ $$ Commented by jagoll last updated on 10/Apr/20 $$\mathscr{L}\left(\mathrm{1}−\mathrm{cos}\:\mathrm{x}\right)\:=\:\mathrm{1}−\frac{\mathrm{x}}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:=\:\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}} \\…
Question Number 88413 by 675480065 last updated on 10/Apr/20 $$\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{dx} \\ $$$$ \\ $$ Commented by abdomathmax last updated on 10/Apr/20…
Question Number 153946 by talminator2856791 last updated on 12/Sep/21 $$\: \\ $$$$\:\:\mathrm{show}\:\mathrm{whether} \\ $$$$\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{sin}\left({x}^{\mathrm{2}} \right)\mathrm{cos}\left(\sqrt{{x}}\right){dx} \\ $$$$\:\:\mathrm{is}\:\mathrm{solvable} \\ $$$$\: \\ $$ Terms of…
Question Number 88388 by M±th+et£s last updated on 10/Apr/20 Answered by mind is power last updated on 10/Apr/20 $$\mathrm{49}{sec}^{\mathrm{2}} \left({x}\right)+\mathrm{28}{tan}\left({x}\right)+\mathrm{9}{sin}^{\mathrm{2}} \left({x}\right)−\mathrm{6}{sin}\left({x}\right)−\mathrm{44} \\ $$$$=\mathrm{49}\left(\mathrm{1}+{tg}^{\mathrm{2}} \left({x}\right)\right)+\mathrm{28}{tg}\left({x}\right)+\left(\mathrm{3}{sin}\left({x}\right)−\mathrm{1}\right)^{\mathrm{2}} −\mathrm{45}…
Question Number 22843 by gourav~ last updated on 22/Oct/17 $${calculate}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1000}} {e}^{{x}−\left[{x}\right]} {dx}\:=? \\ $$$${where}….\:\left[{x}\right]\:{is}\:{greatest}\:{integer}\:{functon} \\ $$ Answered by ajfour last updated on 23/Oct/17 $${let}\:{I}=\int_{\mathrm{0}}…
Question Number 153893 by Tawa11 last updated on 11/Sep/21 $$\int_{\:\mathrm{0}} ^{\:\:\infty} \mathrm{a}\:\underset{\mathrm{p}\:\rightarrow\:\mathrm{1}} {\overset{\infty} {\prod}}\left(\frac{\mathrm{p}^{\mathrm{2}} \:\:−\:\:\:\mathrm{x}^{\mathrm{2n}} }{\mathrm{p}^{\mathrm{2}} }\right)\mathrm{dx},\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}\:\:<\:\:\mathrm{2n}\:\:<\:\:\mathrm{n}\:\:+\:\:\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 88357 by jagoll last updated on 10/Apr/20 $$\int\underset{\mathrm{1}} {\overset{\mathrm{4}} {\:}}\:\frac{\mathrm{dx}}{\left(\mathrm{4x}−\mathrm{1}\right)\sqrt{\mathrm{x}}} \\ $$ Commented by john santu last updated on 10/Apr/20 $$\left[\:{t}=\sqrt{{x}}\:,\:\mathrm{2}{t}\:{dt}\:=\:{dx}\:\right]\: \\ $$$$\underset{\mathrm{1}}…
Question Number 153875 by mnjuly1970 last updated on 11/Sep/21 $$ \\ $$$$\:\:\:\:\mathrm{Prove}\:\:\mathrm{that}.. \\ $$$$\:\:\: \\ $$$$\:\:\:\:\boldsymbol{\phi}\::\:=\int_{\:\mathrm{1}} ^{\:+\infty} \frac{\:{ln}\:\left({x}\:\right)}{\left(\:{x}^{\:\pi} \:−\mathrm{1}\:\right)\left(\:{ln}^{\:\mathrm{2}} \left({x}\right)\:+\mathrm{1}\:\right)^{\mathrm{2}} }{dx}=\:\frac{\pi^{\:\mathrm{2}} −\:\mathrm{8}}{\mathrm{16}}\:\:\:\:\:\:\:\:\:\blacksquare\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\: \\…
Question Number 153873 by mnjuly1970 last updated on 11/Sep/21 $$ \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \frac{\:{x}}{\left(\mathrm{1}\:+{x}^{\:\mathrm{2}} \right)\:\left(\:{e}^{\:\mathrm{2}\pi{x}} −\:\mathrm{1}\right)}\:{dx}\:=\frac{\mathrm{2}\gamma−\:\mathrm{1}}{\mathrm{4}} \\ $$$$ \\ $$ Commented by qaz last updated…