Question Number 132287 by benjo_mathlover last updated on 13/Feb/21 Answered by Olaf last updated on 13/Feb/21 $$\mathrm{Let}\:{q}\:=\:\mathrm{2}\int_{\mathrm{0}} ^{\mathrm{6}} {f}\left({x}\right){dx}\:=\:\mathrm{2}\int_{\mathrm{0}} ^{\mathrm{6}} {f}\left({x}−\mathrm{4}\right){dx}\:\:\:\:\left(\mathrm{1}\right) \\ $$$$\mathrm{Let}\:{u}\:=\:{x}−\mathrm{4} \\ $$$$\left(\mathrm{1}\right)\::\:{q}\:=\:\mathrm{2}\int_{−\mathrm{4}}…
Question Number 66739 by mhmd last updated on 19/Aug/19 $${find}\int\sqrt{{dx}\:} \\ $$ Answered by $@ty@m123 last updated on 19/Aug/19 $${undefind}\:{symbols}. \\ $$ Terms of Service…
Question Number 66740 by behi83417@gmail.com last updated on 19/Aug/19 $$\underset{\:\:\mathrm{0}} {\overset{\:\:\:\:\:\:\:\mathrm{1}} {\int}}\sqrt{\mathrm{1}−\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\boldsymbol{\mathrm{x}}^{\mathrm{3}} \:}\:\:\boldsymbol{\mathrm{dx}}=? \\ $$ Commented by mathmax by abdo last updated on 21/Aug/19…
Question Number 66728 by Tony Lin last updated on 19/Aug/19 $$\int_{\mathrm{1}} ^{\infty} \frac{\mathrm{1}}{{x}\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}=? \\ $$ Commented by mathmax by abdo last updated on 19/Aug/19…
Question Number 66731 by aditya730222@gmail.com last updated on 19/Aug/19 $${y}={x}^{\mathrm{2}} −\mathrm{3}{x}\:\:\:\:\:{y}=\mathrm{2}{x}\:{find}\:{area} \\ $$ Commented by Tony Lin last updated on 19/Aug/19 $${x}^{\mathrm{2}} −\mathrm{3}{x}=\mathrm{2}{x} \\ $$$${x}\left({x}−\mathrm{5}\right)=\mathrm{0}…
Question Number 132235 by bemath last updated on 12/Feb/21 $$\:\mathrm{I}=\:\int\:\frac{\mathrm{3x}+\mathrm{5}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{3}\right)^{\mathrm{2}} }\:\mathrm{dx}\:? \\ $$ Answered by bemath last updated on 12/Feb/21 Commented by bemath last…
Question Number 66695 by mathmax by abdo last updated on 18/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({arctanx}\right)}{\mathrm{4}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by ~ À ® @ 237 ~…
Question Number 66694 by mathmax by abdo last updated on 18/Aug/19 $$\left.{let}\:{f}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{4}} +{x}^{\mathrm{2}} \:+{a}\right)}\:{with}\:{a}\in\right]\frac{\mathrm{1}}{\mathrm{4}},+\infty\left[\right. \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:{g}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\frac{{dx}}{\left({x}^{\mathrm{4}} \:+{x}^{\mathrm{2}} +{a}\right)^{\mathrm{2}} }…
Question Number 66693 by mathmax by abdo last updated on 18/Aug/19 $${calculate}\:\:\int_{−\infty} ^{+\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$ Commented by mathmax by abdo last updated…
Question Number 132192 by benjo_mathlover last updated on 12/Feb/21 $$\:\int\:\frac{\mathrm{dx}}{\mathrm{csc}\:\mathrm{x}\:+\:\mathrm{sec}\:\mathrm{x}} \\ $$ Answered by Dwaipayan Shikari last updated on 12/Feb/21 $$\int\frac{{sinx}\:{cosx}}{{sinx}+{cosx}}{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int{sinx}+{cosx}−\frac{\mathrm{1}}{{sinx}+{cosx}}{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\left({sinx}−{cosx}\right)−\int\frac{{dt}}{\mathrm{1}−{t}^{\mathrm{2}}…