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 $${let}\:{A}\:=\int\:\:\frac{{dx}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}\:\Rightarrow{A}\:=\int\:\:\:\frac{{dx}}{\left({x}−\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} \:+\frac{\mathrm{3}}{\mathrm{4}}}…
Question Number 131527 by Sudip last updated on 05/Feb/21 Answered by Dwaipayan Shikari last updated on 05/Feb/21 $$\frac{\mathrm{2}}{\mathrm{7}}\int\frac{{t}}{{t}+\frac{\mathrm{22}}{\mathrm{7}}}{dt}+\frac{\mathrm{5}}{\mathrm{7}}\int\frac{\mathrm{1}}{{t}+\frac{\mathrm{22}}{\mathrm{7}}}{dt} \\ $$$$=\frac{\mathrm{2}}{\mathrm{7}}{t}−\frac{\mathrm{44}}{\mathrm{49}}{log}\left({t}+\frac{\mathrm{22}}{\mathrm{7}}\right)+\frac{\mathrm{5}}{\mathrm{7}}{log}\left({t}+\frac{\mathrm{22}}{\mathrm{7}}\right) \\ $$ Answered by mr…
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 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 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 $${f}\left({x}\right)=−\mathrm{1} \\ $$$${g}\left({x}\right)=\mathrm{1}…
Question Number 131505 by benjo_mathlover last updated on 05/Feb/21 $$\mathrm{If}\:\int_{\mathrm{a}} ^{\mathrm{b}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\:=\:\int_{\mathrm{a}} ^{\mathrm{b}} \mathrm{g}\left(\mathrm{x}\right)\mathrm{dx} \\ $$$$\mathrm{is}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{g}\left(\mathrm{x}\right)\:?\: \\ $$$$\mathrm{true}\:\mathrm{or}\:\mathrm{false}? \\ $$ Commented by EDWIN88 last updated…