Question Number 64102 by mmkkmm000m last updated on 13/Jul/19 $$\int{tan}\left(\mathrm{1}/{x}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 129635 by pticantor last updated on 17/Jan/21 $$\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\int\frac{\boldsymbol{{dx}}}{\left(\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }=? \\ $$$$\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\sum}}\frac{\mathrm{1}}{\boldsymbol{{k}}\left(\boldsymbol{{k}}+\mathrm{1}\right)\left(\mathrm{2}\boldsymbol{{k}}+\mathrm{1}\right)}=? \\ $$ Commented by liberty…
Question Number 64068 by mathmax by abdo last updated on 12/Jul/19 $${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\frac{{tsint}}{\mathrm{3}+{sin}^{\mathrm{2}} {t}}\:{dt}\: \\ $$ Commented by mathmax by abdo last updated on…
Question Number 64065 by mathmax by abdo last updated on 12/Jul/19 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 129594 by bagjagunawan last updated on 16/Jan/21 Commented by bemath last updated on 17/Jan/21 $$\:\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}+\frac{\mathrm{1}+\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}}{\mathrm{cos}\:\mathrm{x}\:\mathrm{sin}\:\mathrm{x}}\:=\: \\ $$$$\:\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\:+\frac{\mathrm{2cos}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\left(\mathrm{sin}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\right)}{\mathrm{2sin}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\mathrm{cos}\:\mathrm{x}}\:= \\ $$$$\:\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}+\frac{\mathrm{1}}{\mathrm{sin}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\left(\mathrm{cos}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)−\mathrm{sin}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\right)}= \\ $$$$\:\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\:+\:\frac{\mathrm{2}}{\mathrm{sin}\:\mathrm{x}−\mathrm{1}+\mathrm{cos}\:\mathrm{x}}= \\ $$$$\:\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}+\:\frac{\mathrm{2}}{\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}−\mathrm{1}}=\frac{\left(\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}}…
Question Number 129576 by greg_ed last updated on 16/Jan/21 $$\boldsymbol{\mathrm{please}},\:\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{f}}\::\:\left[\mathrm{0}\:,\:\boldsymbol{{a}}\right]\:×\:\mathbb{R}_{+} \:\rightarrow\:\mathbb{R} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\boldsymbol{{x}},\:\boldsymbol{{y}}\right)\:\:\:\:\:\:\: \:\:\boldsymbol{{e}}^{−\boldsymbol{{xy}}} \:\boldsymbol{{sin}}\:\boldsymbol{{x}}\: \\ $$$$\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{integrable}}\:???\: \\ $$ Answered by mathmax by…
Question Number 64037 by MJS last updated on 18/Nov/19 $$\mathrm{reduction}\:\mathrm{formulas}\:\mathrm{for}\:{n}\in\mathbb{N},\:\mathrm{some}\:{n}>\mathrm{0},\:\mathrm{some}\:{n}>\mathrm{1} \\ $$$$ \\ $$$$\int\mathrm{sin}^{{n}} \:{x}\:{dx}=−\frac{\mathrm{1}}{{n}}\mathrm{cos}\:{x}\:\mathrm{sin}^{{n}−\mathrm{1}} \:{x}\:+\frac{{n}−\mathrm{1}}{{n}}\int\mathrm{sin}^{{n}−\mathrm{2}} \:{x}\:{dx} \\ $$$$\int\mathrm{cos}^{{n}} \:{x}\:{dx}=\frac{\mathrm{1}}{{n}}\mathrm{sin}\:{x}\:\mathrm{cos}^{{n}−\mathrm{1}} \:{x}\:+\frac{{n}−\mathrm{1}}{{n}}\int\mathrm{cos}^{{n}−\mathrm{2}} \:{x}\:{dx} \\ $$$$\int\mathrm{tan}^{{n}} \:{x}\:{dx}=\frac{\mathrm{1}}{{n}−\mathrm{1}}\mathrm{tan}^{{n}−\mathrm{1}}…
Question Number 129562 by mathmax by abdo last updated on 16/Jan/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{6}} +\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Answered by Lordose last updated on 16/Jan/21…
Question Number 129564 by bramlexs22 last updated on 16/Jan/21 $$\:\mathcal{V}\:=\:\int\:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{sin}\:\left(\mathrm{x}+\theta\right)}\:\mathrm{dx}\: \\ $$ Answered by Lordose last updated on 16/Jan/21 $$\Omega\:=\:\int\frac{\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{sin}\left(\mathrm{x}+\theta\right)}\mathrm{dx}\:\overset{\mathrm{u}=\mathrm{x}+\theta} {=}\int\frac{\mathrm{sin}\left(\mathrm{u}−\theta\right)}{\mathrm{sin}\left(\mathrm{u}\right)}\mathrm{du} \\ $$$$\Omega\:=\:\int\frac{\mathrm{sin}\left(\mathrm{u}\right)\mathrm{cos}\theta−\mathrm{cos}\left(\mathrm{u}\right)\mathrm{sin}\theta}{\mathrm{sin}\left(\mathrm{u}\right)}\mathrm{du}\:=\:\mathrm{ucos}\theta\:−\:\mathrm{sin}\theta\mathrm{ln}\left(\mathrm{sinu}\right)\:+\:\mathrm{C} \\ $$$$\Omega\:=\:\left(\mathrm{x}+\theta\right)\mathrm{cos}\theta\:−\:\mathrm{sin}\theta\mathrm{ln}\left(\mathrm{sin}\left(\mathrm{x}+\theta\right)\right)+\:\mathrm{C}…
Question Number 129558 by mnjuly1970 last updated on 16/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{modern}\:\ast\ast\ast\ast\ast\ast\ast\ast\ast\ast\:{algebra}\:…\: \\ $$$$\:\:\:\:\:\:\:\::::\:\:{if}\:\:''\:{G}\:''\:{be}\:{a}\:{finite}\:{group}\:{and} \\ $$$$\:\:{O}\:\left({G}\right)={pq}\:\:,\:\:{where}\:''\:{p}\:,\:{q}\:''\:{are}\:{two} \\ $$$$\:\:{prime}\:\:{numbers}\:\left({p}\:>\:{q}\:\right)\:{then}\:{prove}\:{that}: \\ $$$$\:\:{G}\:\:{has}\:\:{at}\:{most}\:{one}\:{subgroup}\:{of}\:{order}\:''\:{p}\:''\:. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{written}\:{and}\:{compiled}\:{by} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\clubsuit{m}.{n}.{july}.\mathrm{1970}\clubsuit…. \\ $$ Answered…