Question Number 86013 by mathmax by abdo last updated on 26/Mar/20 $${calculate}\:\:\int_{\mathrm{1}+\sqrt{\mathrm{2}}} ^{+\infty} \:\:\:\:\frac{{dx}}{\left({x}−\mathrm{1}\right)^{\mathrm{3}} \left({x}+\mathrm{2}\right)^{\mathrm{3}} } \\ $$ Commented by mathmax by abdo last updated…
Question Number 20471 by ajfour last updated on 27/Aug/17 $${Find}\:{the}\:{surface}\:{area}\:{of}\:{a}\:{solid} \\ $$$${that}\:{is}\:{common}\:{part}\:{of}\:{two} \\ $$$${cylinders}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={a}^{\mathrm{2}} ,\:{y}^{\mathrm{2}} +{z}^{\mathrm{2}} ={a}^{\mathrm{2}} . \\ $$$$\boldsymbol{{Compute}}\:\boldsymbol{{the}}\:\boldsymbol{{volume}}\:\boldsymbol{{also}}. \\ $$ Commented…
Question Number 20468 by tammi last updated on 27/Aug/17 $$\int\frac{{dx}}{\mathrm{sin}\:^{\mathrm{4}} {x}−\mathrm{cos}\:^{\mathrm{4}} {x}} \\ $$ Answered by ajfour last updated on 27/Aug/17 $$−\int\mathrm{sec}\:\mathrm{2}{xdx}=−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\mid\mathrm{sec}\:\mathrm{2}{x}+\mathrm{tan}\:\mathrm{2}{x}\mid+{C}\:. \\ $$ Terms…
Question Number 20467 by tammi last updated on 27/Aug/17 $$\int\left({a}\mathrm{sin}\:^{\mathrm{2}} {x}+{b}\mathrm{cos}\:^{\mathrm{2}} {x}\right){dx} \\ $$ Answered by ajfour last updated on 27/Aug/17 $$=\frac{{a}}{\mathrm{2}}\int\left(\mathrm{1}−\mathrm{cos}\:\mathrm{2}{x}\right){dx}+\frac{{b}}{\mathrm{2}}\int\left(\mathrm{1}+\mathrm{cos}\:\mathrm{2}{x}\right){dx} \\ $$$$=\frac{{a}}{\mathrm{2}}\left({x}−\frac{\mathrm{sin}\:\mathrm{2}{x}}{\mathrm{2}}\right)+\frac{{b}}{\mathrm{2}}\left({x}+\frac{\mathrm{sin}\:\mathrm{2}{x}}{\mathrm{2}}\right)+{C} \\…
Question Number 20465 by tammi last updated on 27/Aug/17 $$\int\frac{\mathrm{cos}\:\mathrm{2}{xdx}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}{x}+\mathrm{8}} \\ $$ Answered by sma3l2996 last updated on 27/Aug/17 $${t}={sin}\left(\mathrm{2}{x}\right)\Rightarrow{dt}=\mathrm{2}{cos}\left(\mathrm{2}{x}\right){dx} \\ $$$$\int\frac{{cos}\mathrm{2}{xdx}}{{sin}^{\mathrm{2}} \mathrm{2}{x}+\mathrm{8}}=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{dt}}{{t}^{\mathrm{2}} +\mathrm{8}}=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{dt}}{\mathrm{8}\left(\left(\frac{{t}}{\mathrm{2}\sqrt{\mathrm{2}}}\right)^{\mathrm{2}}…
Question Number 20466 by tammi last updated on 27/Aug/17 $$\int\frac{\mathrm{sin}\:{x}\mathrm{cos}\:{xdx}}{\mathrm{sin}^{\mathrm{4}} {x}+\mathrm{cos}\:^{\mathrm{4}} {x}} \\ $$ Answered by sma3l2996 last updated on 27/Aug/17 $${t}={sin}^{\mathrm{2}} {x}\Rightarrow{dt}=\mathrm{2}{sinxcosxdx} \\ $$$${I}=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{dt}}{{t}^{\mathrm{2}}…
Question Number 85999 by M±th+et£s last updated on 26/Mar/20 $$\int_{\mathrm{0}} ^{\infty} \frac{{sinx}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{4}} }{dx}=\mathrm{0}.\mathrm{4009} \\ $$$${prove}\:{that} \\ $$ Commented by MJS last updated on 26/Mar/20…
Question Number 20456 by tammi last updated on 27/Aug/17 $$\int\mathrm{cot}\:^{\mathrm{4}} {xdx} \\ $$ Commented by Joel577 last updated on 27/Aug/17 $${use}\:\mathrm{cot}^{\mathrm{2}} \:{x}\:=\:\mathrm{cosec}^{\mathrm{2}} \:{x}\:−\:\mathrm{1} \\ $$…
Question Number 20454 by tammi last updated on 27/Aug/17 $$\int\mathrm{sec}\:^{\mathrm{3}} {xdx} \\ $$ Commented by Joel577 last updated on 27/Aug/17 $${u}\:{can}\:{use}\:{reduction}\:{formula}\:{for}\:\int\:{sec}^{{n}} \:{x}\:{dx} \\ $$ Terms…
Question Number 20455 by tammi last updated on 27/Aug/17 $$\int{sec}^{\mathrm{6}} {xdx} \\ $$ Commented by Joel577 last updated on 27/Aug/17 $${use}\:{reduction}\:{formula} \\ $$ Terms of…