Question Number 101451 by yahyajan last updated on 02/Jul/20 Commented by Dwaipayan Shikari last updated on 02/Jul/20 $${sin}^{−\mathrm{1}} {x}\int\mathrm{1}{dx}−\int\frac{{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx} \\ $$$${xsin}^{−\mathrm{1}} {x}\:+\frac{\mathrm{1}}{\mathrm{2}}\int\frac{−\mathrm{2}{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx}\:\:\:={xsin}^{−\mathrm{1}} {x}+\sqrt{\mathrm{1}−{x}^{\mathrm{2}}…
Question Number 35909 by ajfour last updated on 25/May/18 $$\int\frac{\mathrm{7}{x}−\mathrm{6}}{\left({x}^{\mathrm{2}} +\mathrm{25}\right)\sqrt{\left({x}−\mathrm{3}\right)^{\mathrm{2}} +\mathrm{4}}}\:{dx}\:=\:? \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 26/May/18 $${this}\:{nut}\:{is}\:{hard}\:{to}\:{crack}…{i}\:{am}\:{fighting}..{hope} \\ $$$${reach}\:{the}\:{destination}\:{to}\:{get}\:{it}\:{solved}… \\…
Question Number 166956 by mnjuly1970 last updated on 03/Mar/22 $$ \\ $$$$\:\:\:\:{calculate} \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{\sqrt{{x}}\:{arctan}\left({x}\right)}{\mathrm{1}+{x}^{\:\mathrm{2}} }{dx}\:=? \\ $$ Answered by ArielVyny last updated on…
Question Number 166959 by cortano1 last updated on 03/Mar/22 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\gamma=\int\:\frac{\mathrm{e}^{\mathrm{x}} \left(\mathrm{sin}\:\mathrm{x}+\mathrm{1}\right)}{\mathrm{cos}\:\mathrm{x}+\mathrm{1}}\:\mathrm{dx}\:=? \\ $$ Answered by ArielVyny last updated on 03/Mar/22 $$\gamma=\int\frac{{e}^{{x}} \left({sinx}+\mathrm{1}\right)}{{cosx}+\mathrm{1}}{dx} \\ $$$${t}={tan}\left(\frac{{x}}{\mathrm{2}}\right)\rightarrow\mathrm{2}{arctan}\left({t}\right)={x} \\…
Question Number 166940 by cortano1 last updated on 03/Mar/22 Answered by som(math1967) last updated on 03/Mar/22 $$\int\frac{{e}^{{x}} {x}+{e}^{{x}} }{{xe}^{{x}} \left(\mathrm{1}+{xe}^{{x}} \right)}{dx} \\ $$$${let}\:\:{xe}^{{x}} ={z}\Rightarrow\left({xe}^{{x}} +{e}^{{x}}…
Question Number 166939 by cortano1 last updated on 03/Mar/22 Answered by som(math1967) last updated on 03/Mar/22 $$\int\frac{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} −\mathrm{2}{x}^{\mathrm{2}} }{{x}^{\mathrm{6}} +\mathrm{1}}{dx} \\ $$$$\int\frac{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{\left({x}^{\mathrm{2}}…
Question Number 166916 by mnjuly1970 last updated on 02/Mar/22 $$ \\ $$$$\:\:\:\:\:\Omega=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:{H}_{\:{n}} }{{n}\left({n}+\mathrm{1}\right)}\:= \\ $$$$\:\:\:\:\:\:\:−−−−−− \\ $$$$\:\:\:\:\:\:\:\Omega\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}−\frac{\mathrm{1}}{{n}+\mathrm{1}}\:\int_{\mathrm{0}\:} ^{\:\mathrm{1}} {x}^{\:{n}−\mathrm{1}} {ln}\left(\mathrm{1}−{x}\:\right){dx} \\…
Question Number 101378 by Rohit@Thakur last updated on 02/Jul/20 $$\int_{\frac{\mathrm{1}}{{e}}} ^{{tanx}} \frac{{t}}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:+\:\int_{\frac{\mathrm{1}}{{e}}} ^{{cotx}} \frac{\mathrm{1}}{{t}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{dt} \\ $$ Commented by Dwaipayan Shikari last updated on…
Question Number 101373 by Dwaipayan Shikari last updated on 02/Jul/20 $$\underset{{n}\rightarrow\infty\:} {\mathrm{lim}}\underset{{r}=\mathrm{1}} {\overset{\mathrm{4}{n}} {\sum}}\frac{\sqrt{{n}}}{\:\sqrt{{r}}\left(\mathrm{3}\sqrt{{r}}+\mathrm{4}\sqrt{{n}}\right)^{\mathrm{2}} } \\ $$ Commented by Dwaipayan Shikari last updated on 02/Jul/20…
Question Number 35832 by abdo mathsup 649 cc last updated on 24/May/18 $${find}\:{the}\:{value}\:{of}\:\:{f}\left(\lambda\right)\:=\:\int_{−{a}} ^{{a}} \:\:\:\frac{{dx}}{\left(\lambda\:+_{} {x}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} } \\ $$$$\lambda\in{R}\:. \\ $$ Commented by abdo.msup.com…