Question Number 152105 by talminator2856791 last updated on 25/Aug/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{1}}{\lfloor{x}+\mathrm{1}\rfloor}\:−\:\frac{\mathrm{1}}{{x}+\mathrm{1}}\:{dx} \\ $$$$\: \\ $$ Answered by Olaf_Thorendsen last updated on 25/Aug/21…
Question Number 152110 by peter frank last updated on 25/Aug/21 $$\int\mathrm{a}^{\mathrm{mx}} \mathrm{b}^{\mathrm{nx}} \mathrm{dx} \\ $$ Answered by peter frank last updated on 25/Aug/21 $$\int\left(\mathrm{a}^{\mathrm{m}} \mathrm{b}^{\mathrm{n}}…
Question Number 152094 by mnjuly1970 last updated on 25/Aug/21 Answered by Olaf_Thorendsen last updated on 25/Aug/21 $$\mathrm{7cos}{x}+\mathrm{4sin}{x}+\mathrm{5}\:=\:\mathrm{0}\:\:\:\:\left(\mathrm{1}\right) \\ $$$$\mathrm{Let}\:{t}\:=\:\mathrm{tan}\frac{{x}}{\mathrm{2}} \\ $$$$\left(\mathrm{1}\right)\::\:\mathrm{7}\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }+\mathrm{4}\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }+\mathrm{5}\:=\:\mathrm{0} \\…
Question Number 152088 by rexford last updated on 25/Aug/21 $$\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}} \mid{sinx}−{cosx}\mid \\ $$$${please}\:{help}\:{me}\:{out} \\ $$ Answered by Olaf_Thorendsen last updated on 25/Aug/21 $$\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 86518 by john santu last updated on 29/Mar/20 $$\int\:\:\frac{\mathrm{dx}}{\mathrm{e}^{\mathrm{2x}} −\mathrm{5e}^{\mathrm{x}} } \\ $$ Commented by john santu last updated on 29/Mar/20 $$\Rightarrow\:\int\:\:\frac{\mathrm{dx}}{\mathrm{e}^{\mathrm{x}} \:\left(\mathrm{e}^{\mathrm{x}}…
Question Number 152047 by talminator2856791 last updated on 25/Aug/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{{x}^{\mathrm{2}} +\mathrm{1}}{\:\sqrt{{x}^{{x}} }}\:{dx} \\ $$$$\: \\ $$ Terms of Service Privacy Policy…
Question Number 86491 by john santu last updated on 29/Mar/20 $$\int\:\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}{\mathrm{x}^{\mathrm{4}} +\mathrm{1}}\:\mathrm{dx}\:?\: \\ $$ Commented by john santu last updated on 29/Mar/20 $$\mathrm{dear}\:\mathrm{prof}\:\mathrm{mr}\:\mathrm{mjs}.\:\mathrm{what}\:\mathrm{the}\:\mathrm{super} \\…
Question Number 86484 by Ar Brandon last updated on 28/Mar/20 $$\int\frac{{x}^{\mathrm{6}} }{\mathrm{1}+{x}^{\mathrm{12}} }{dx} \\ $$ Commented by Ar Brandon last updated on 29/Mar/20 Hi mathmax, I don't understand the second line of your solution. How did you do that ? Commented…
Question Number 86480 by M±th+et£s last updated on 28/Mar/20 $$\int_{\mathrm{0}} ^{\infty} \left({x}\:{e}^{\mathrm{1}−{x}} \:−\lfloor{x}\rfloor{e}^{\mathrm{1}−\lfloor{x}\rfloor} \right){dx} \\ $$ Commented by abdomathmax last updated on 28/Mar/20 $${I}\:=\int_{\mathrm{0}} ^{\infty}…
Question Number 20939 by Hitler last updated on 08/Sep/17 $$\mathrm{Demostration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{an}\:\mathrm{sphere}\:\mathrm{V}=\frac{\mathrm{4}\pi\mathrm{r}^{\mathrm{3}} }{\mathrm{3}} \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{r}^{\mathrm{2}} \:\mathrm{We}\:\mathrm{divide}\:\mathrm{the}\:\mathrm{sphere}\:\mathrm{in}\:\mathrm{8}\:\mathrm{parts}.\:\mathrm{So}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{a}\:\mathrm{part}\:\mathrm{is} \\ $$$$\int_{\mathrm{0}} ^{\:\mathrm{r}} \int_{\mathrm{0}} ^{\:\sqrt{\mathrm{r}^{\mathrm{2}} −\mathrm{x}^{\mathrm{2}} }} \sqrt{\mathrm{r}^{\mathrm{2}}…