Question Number 65988 by mmkkmm000m last updated on 07/Aug/19 $$\int{dx}/{x}^{\mathrm{2}} −{x}+\mathrm{1} \\ $$ Commented by mathmax by abdo last updated on 07/Aug/19 $${let}\:{A}\:=\int\:\:\frac{{dx}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}\:\Rightarrow{A}\:=\int\:\:\:\frac{{dx}}{\left({x}−\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} \:+\frac{\mathrm{3}}{\mathrm{4}}}…
Question Number 453 by Karting7442 last updated on 25/Jan/15 $${solve}\:{for}\:{x}\:\:\:\mathrm{3}\left(\mathrm{14}{x}−\mathrm{15}\right)=−\mathrm{72} \\ $$ Answered by prakash jain last updated on 09/Jan/15 $$\mathrm{3}\left(\mathrm{14}{x}−\mathrm{15}\right)=−\mathrm{72} \\ $$$$\mathrm{42}{x}−\mathrm{45}=−\mathrm{72} \\ $$$$\mathrm{42}{x}=−\mathrm{72}+\mathrm{45}…
Question Number 451 by Karting7442 last updated on 25/Jan/15 $${solve}\:{the}\:{equation}\:{for}\:{x}\:\::\:\mathrm{5}−{x}=\:−\mathrm{3} \\ $$ Answered by prakash jain last updated on 09/Jan/15 $$\mathrm{5}−{x}=−\mathrm{3} \\ $$$${x}=\mathrm{5}+\mathrm{3}=\mathrm{8} \\ $$…
Question Number 131520 by EDWIN88 last updated on 05/Feb/21 $$\:\mathrm{Nice}\:\mathrm{integral}\: \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{x}^{\mathrm{2}} }{\left(\mathrm{x}+\mathrm{100}\right)^{\mathrm{3}} }\:\mathrm{dx}\:=? \\ $$ Commented by liberty last updated on 05/Feb/21…
Question Number 449 by 123456 last updated on 25/Jan/15 $$\mathrm{if}\:\mid{z}\mid=\mathrm{1},{z}\in\mathbb{C},{a}\in\mathbb{R} \\ $$$$\mathrm{find}\:\mathrm{max}\:\mathrm{value}\:\mathrm{of}\:\mid{z}^{\mathrm{2}} +{az}−\mathrm{1}\mid \\ $$ Answered by prakash jain last updated on 09/Jan/15 $${z}={i} \\…
Question Number 131517 by benjo_mathlover last updated on 05/Feb/21 $$\mathrm{Given}\:\int_{\mathrm{0}} ^{\mathrm{3}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=\int_{\mathrm{0}} ^{\mathrm{3}} \left(\mathrm{2x}−\mathrm{1}\right)\mathrm{dx}+\int_{\mathrm{0}} ^{\mathrm{3}} \left(\int_{\mathrm{0}} ^{\mathrm{3}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\right)\mathrm{dx} \\ $$$$\mathrm{find}\:\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\:. \\ $$ Answered…
Question Number 65983 by Rio Michael last updated on 07/Aug/19 $$\:{Simplify}\: \\ $$$$\:\:\:\left(\mathrm{1}+\:\mathrm{2}{i}\sqrt{\mathrm{2}}\right)^{\mathrm{7}} \:−\:\left(\mathrm{1}\:+\mathrm{2}{i}\right)^{\mathrm{7}} \\ $$ Commented by Rio Michael last updated on 17/Aug/19 $${can}\:{i}\:{use}\:{de}\:{moivre}'{s}\:{theorem}?…
Question Number 65980 by Tony Lin last updated on 07/Aug/19 Commented by Tanmay chaudhury last updated on 07/Aug/19 Answered by Tanmay chaudhury last updated on…
Question Number 445 by 123456 last updated on 05/Jan/15 $$\mathrm{0}\leqslant\mid{f}\left({x}\right)\mid\leqslant\mid{g}\left({x}\right)\mid \\ $$$$\int{g}\left({x}\right)−{f}\left({x}\right)\:{dx}\leqslant\int{f}\left({x}\right)+{g}\left({x}\right)\:{dx}\:\:? \\ $$ Commented by prakash jain last updated on 05/Jan/15 $${f}\left({x}\right)=−\mathrm{1} \\ $$$${g}\left({x}\right)=\mathrm{1}…
Question Number 65981 by Tanmay chaudhury last updated on 07/Aug/19 Answered by jimful last updated on 07/Aug/19 $${let}\:{s}_{{n}} =\Sigma\mathrm{1}/{n}. \\ $$$$\Sigma\left({k}+\mathrm{1}\right)/{k}\:\bullet\Sigma{k}/\left({k}+\mathrm{1}\right) \\ $$$$=\left({n}+{s}_{{n}} \right)\left({n}−{s}_{{n}+\mathrm{1}} +\mathrm{1}\right)…