Question Number 36649 by rahul 19 last updated on 03/Jun/18 $$\int\:\frac{\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{1}}\:{dx} \\ $$ Commented by rahul 19 last updated on 03/Jun/18 $$\int\:\frac{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }}{{x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}}…
Question Number 167716 by cortano1 last updated on 23/Mar/22 Answered by mahdipoor last updated on 23/Mar/22 $$\Rightarrow \\ $$$${f}^{\:'} \left({x}\right)={cosx}+{f}^{\:'} \left({x}\right)\left(\mathrm{2}{sinx}−{sin}^{\mathrm{2}} {x}\right) \\ $$$$\Rightarrow{f}^{\:'} \left({x}\right)=\frac{{cosx}}{\mathrm{1}+{sin}^{\mathrm{2}}…
Question Number 102183 by bemath last updated on 07/Jul/20 $$\int\:\frac{\mathrm{cos}\:\theta}{\mathrm{sin}\:\theta−\mathrm{cos}\:\theta}\:{d}\theta\:? \\ $$ Answered by Dwaipayan Shikari last updated on 07/Jul/20 $$\frac{\mathrm{1}}{\mathrm{2}}{log}\left({sin}\theta−{cos}\theta\right)−\frac{\theta}{\mathrm{2}}+{C} \\ $$$${I}=\int\frac{{cos}\theta}{{sin}\theta−{cos}\theta}{d}\theta \\ $$$${I}=\int\frac{{sin}\theta}{{sin}\theta−{cos}\theta}−\mathrm{1}{d}\theta…
Question Number 36643 by rahul 19 last updated on 03/Jun/18 $$\int\:\frac{{x}}{{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}}\:{dx}\:=\:? \\ $$ Commented by math khazana by abdo last updated on 09/Aug/18…
Question Number 167713 by infinityaction last updated on 23/Mar/22 Answered by Nimatullah last updated on 23/Mar/22 $$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}}{{x}+\mathrm{1}}{dx}=\mathrm{ln}\left[{x}+\mathrm{1}\right]_{\mathrm{0}} ^{\infty} =\infty \\ $$ Terms of…
Question Number 36633 by abdo.msup.com last updated on 03/Jun/18 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\left({x}^{\mathrm{2}} \:+{x}+\mathrm{1}\right){dx} \\ $$ Commented by abdo.msup.com last updated on 05/Jun/18 $${let}\:{integrate}\:{by}\:{parts} \\ $$$${I}\:=\:\left[\:{x}\:{arctan}\left({x}^{\mathrm{2}}…
Question Number 102169 by bemath last updated on 07/Jul/20 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{x}^{\mathrm{3}/\mathrm{2}} \:\sqrt{\mathrm{1}−{x}}\:{dx}\:? \\ $$ Answered by bemath last updated on 07/Jul/20 Answered by john…
Question Number 102165 by mathmax by abdo last updated on 07/Jul/20 $$\mathrm{calculate}\:\int_{−\infty} ^{\infty} \:\:\frac{\mathrm{x}^{\mathrm{2}} \mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$ Answered by MAB last updated on…
Question Number 102163 by mathmax by abdo last updated on 07/Jul/20 $$\mathrm{solve}\:\:\mathrm{y}^{''} \:−\mathrm{2xy}^{'} \:\:=\mathrm{xe}^{−\mathrm{x}^{\mathrm{2}} } \\ $$ Answered by mathmax by abdo last updated on…
Question Number 102160 by mathmax by abdo last updated on 07/Jul/20 $$\left.\mathrm{1}\right)\:\mathrm{let}\:\mathrm{a}<\mathrm{1}\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\pi} \:\frac{\mathrm{cos}\theta\mathrm{d}\theta}{\left(\mathrm{a}^{\mathrm{2}} −\mathrm{2acos}\theta\:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{\mathrm{cos}\theta}{\left(\mathrm{4}−\mathrm{2}\sqrt{\mathrm{3}}\mathrm{cos}\theta\right)^{\mathrm{2}} }\mathrm{d}\theta \\ $$$$ \\ $$…