Question Number 144419 by mnjuly1970 last updated on 25/Jun/21 $$\:\:\:\:\:…{Advanced}\:….{Calculus}… \\ $$$${Without}\:{using}\:{the}\:{Feynman}'{s}\:{trick}\:, \\ $$$$\:\:\:\:\:{Find}\:{the}\:{value}\:{of}\:\:\::: \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{I}\::=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{Log}\:\left(\mathrm{1}+\:\mathrm{x}^{\:\mathrm{2}} \right)}{\mathrm{1}\:+\mathrm{x}}\:\mathrm{dx}=? \\ $$$$\:\:\:\:\mathrm{m}.\mathrm{n}… \\ $$…
Question Number 144409 by liberty last updated on 25/Jun/21 $$\:\:\:\:\int\:\frac{\mathrm{dx}}{\left(\mathrm{x}+\mathrm{3}\right)\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:? \\ $$ Answered by iloveisrael last updated on 25/Jun/21 $$\:\mathrm{let}\:\mathrm{x}=\mathrm{sin}\:\mathrm{t}\: \\ $$$$\mathrm{I}=\int\:\frac{\mathrm{cos}\:\mathrm{t}}{\left(\mathrm{3}+\mathrm{sin}\:\mathrm{t}\right)\sqrt{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} \mathrm{t}}}\:\mathrm{dt} \\…
Question Number 144402 by rexford last updated on 25/Jun/21 Commented by justtry last updated on 25/Jun/21 Commented by rexford last updated on 27/Jun/21 $${thanks}\:{very}\:{much}\:{for}\:{your}\:{time} \\…
Question Number 78853 by mind is power last updated on 21/Jan/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\left(\mathrm{x}\right)+\mathrm{sin}\left(\mathrm{y}\right)}{\mathrm{x}+\mathrm{y}}\mathrm{dxdy}? \\ $$ Answered by mind is power last updated…
Question Number 78829 by jagoll last updated on 21/Jan/20 $$\mathrm{given}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{x}+\mathrm{4}\right)\:\forall\mathrm{x}\in\mathbb{R} \\ $$$$\mathrm{and}\:\underset{\mathrm{5}} {\overset{\mathrm{7}} {\int}}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=\mathrm{p}\:.\:\mathrm{what}\:\mathrm{is}\: \\ $$$$\underset{\mathrm{2}} {\overset{\mathrm{10}} {\int}}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}? \\ $$$$ \\ $$ Commented by jagoll…
Question Number 144348 by ArielVyny last updated on 24/Jun/21 Commented by Dwaipayan Shikari last updated on 24/Jun/21 $${See}\:{Q}\mathrm{144057} \\ $$ Commented by ArielVyny last updated…
Question Number 78797 by TawaTawa last updated on 20/Jan/20 $$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\int_{\:\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{e}^{\mathrm{x}} \:−\:\mathrm{1}}\:\mathrm{dx}\:\:\:\:=\:\:\:\frac{\pi^{\mathrm{4}} }{\mathrm{15}} \\ $$ Answered by mind is power last updated on…
Question Number 144323 by qaz last updated on 24/Jun/21 $$\underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}+\mathrm{1}} }{\mathrm{n}}=? \\ $$ Answered by mathmax by abdo last updated on 25/Jun/21 $$\mathrm{A}_{\mathrm{n}}…
Question Number 144322 by qaz last updated on 24/Jun/21 $$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{2n}\right)!!}{\left(\mathrm{2n}+\mathrm{1}\right)!!\left(\mathrm{n}+\mathrm{1}\right)}\mathrm{x}^{\mathrm{2n}+\mathrm{2}} =?……….\mid\mathrm{x}\mid\leqslant\mathrm{1} \\ $$ Answered by mindispower last updated on 25/Jun/21 $$\left(\mathrm{2}{n}\right)!!=\mathrm{2}^{{n}} .{n}! \\…
Question Number 78766 by M±th+et£s last updated on 20/Jan/20 $$\int\mathrm{2}\:{e}^{\frac{\mathrm{1}}{\mathrm{2}\left({x}−\mathrm{2}\right)^{\mathrm{2}} }} \:{dx} \\ $$ Answered by MJS last updated on 20/Jan/20 $$\mathrm{2}\int\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{2}\left({x}−\mathrm{2}\right)^{\mathrm{2}} }} {dx}= \\…