Question Number 5628 by sanusihammed last updated on 23/May/16 $${If}\:\:\:{siny}\:=\:{xsin}\left({a}\:+\:{y}\right) \\ $$$$ \\ $$$${Show}\:{that}\:\:\frac{{dy}}{{dx}}\:\:=\:\:\frac{{sin}^{\mathrm{2}} \left({a}\:+\:{y}\right)}{{sina}} \\ $$$$ \\ $$$$ \\ $$$${Please}\:{help}.\:{Thanks}\:{in}\:{advance}. \\ $$ Terms of…
Question Number 136680 by aupo14 last updated on 24/Mar/21 Answered by Olaf last updated on 24/Mar/21 $$\mathrm{F}\left({x}\right)\:=\:\int\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{9}\right)^{\mathrm{2}} } \\ $$$$\mathrm{Let}\:{x}\:=\:\mathrm{3sh}{u} \\ $$$$\mathrm{F}\left({u}\right)\:=\:\int\frac{\mathrm{3ch}{u}}{\left(\mathrm{9sh}^{\mathrm{2}} +\mathrm{9}\right)^{\mathrm{2}} }\:{du}…
Question Number 71142 by mathmax by abdo last updated on 12/Oct/19 $${find}\:\int\sqrt{{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)}{dx} \\ $$ Commented by MJS last updated on 12/Oct/19 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{we}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{this} \\ $$ Terms…
Question Number 136651 by mhabs last updated on 24/Mar/21 Answered by Ñï= last updated on 24/Mar/21 $$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{\mathrm{1}}{\mathrm{1}+\left({a}\mathrm{tan}\:{x}\right)^{\mathrm{2}} }{dx}\overset{{t}=\mathrm{tan}\:{x}} {=}\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}}{\mathrm{1}+{a}^{\mathrm{2}} {t}^{\mathrm{2}} }\centerdot\frac{\mathrm{1}}{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 136644 by mnjuly1970 last updated on 24/Mar/21 $$ \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$$$\:\:\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{log}\left({ax}^{\mathrm{2}} +\mathrm{1}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$$$\:\:\:\:{f}\:'\left({a}\right)=\int_{\mathrm{0}} ^{\:\mathrm{1}}…
Question Number 136626 by mnjuly1970 last updated on 24/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:……….{nice}\:\:\:\:{calculus}……… \\ $$$$\:\:\:\:{suppose}\:{that}::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\varphi\left({p}\right)=\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left(\mathrm{1}+{x}\right)}{\left({p}+{x}\right)^{\mathrm{2}} }\:…\checkmark \\ $$$$\:\:\:\:\:\:\:\:\:\:{find}\:{the}\:{value}\:{of}:: \\ $$$$\:\:\:\:\:\:\:\underset{\mathrm{0}} {\int}^{\:\mathrm{1}} \:\frac{\varphi\left({p}\right)}{\mathrm{1}+{p}}{dp}=?… \\ $$$$\:\:\:\:\:\:…
Question Number 71091 by Henri Boucatchou last updated on 11/Oct/19 Commented by Prithwish sen last updated on 11/Oct/19 $$\boldsymbol{\mathrm{It}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{same}}\:\boldsymbol{\mathrm{as}} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{tan}}^{−\mathrm{1}} \sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}+\mathrm{1}}\:\boldsymbol{\mathrm{dx}}\:−\int_{\mathrm{0}}…
Question Number 5505 by Kasih last updated on 17/May/16 $${if}\:{the}\:{degree}\:{of}\:{the}\:{polynomial}\:{p}\left({x}\right)\:{is}\:{less}\:{than} \\ $$$${the}\:{degree}\:{of}\:{q}\left({x}\right)\:{then}\:{f}\left({x}\right)=\frac{{p}\left({x}\right)}{{q}\left({x}\right)}\:{is}\:{called}\:{a}\:.\:.\:.. \\ $$$${rational}\:{function} \\ $$$$ \\ $$ Commented by Rasheed Soomro last updated on…
Question Number 5506 by Kasih last updated on 17/May/16 $${to}\:{integrate}\:{the}\:{improper}\:{rational}\:{function} \\ $$$${f}\left({x}\right)=\frac{\left({x}^{\mathrm{2}} +\mathrm{4}\right)}{\left({x}+\mathrm{1}\right)}\:{we}\:{first}\:{rewrite}\:{it}\:{as}\:{f}\left({x}\right)=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 5507 by Kasih last updated on 17/May/16 $${if}\:\left({x}−\mathrm{1}\right)\:\left({x}+\mathrm{1}\right)\:+\mathrm{3}{x}+{x}^{\mathrm{2}} ={ax}^{\mathrm{2}} +{bx}+{c}\:{then}\:{a}=?\:{b}=?\:{c}=? \\ $$ Answered by Rasheed Soomro last updated on 17/May/16 $$\:\left({x}−\mathrm{1}\right)\:\left({x}+\mathrm{1}\right)\:+\mathrm{3}{x}+{x}^{\mathrm{2}} ={ax}^{\mathrm{2}} +{bx}+{c}…