Question Number 87793 by M±th+et£s last updated on 06/Apr/20 $${show}\:{that} \\ $$$$\int{e}^{{sin}\left({x}\right)} \:{dx}= \\ $$$$−\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}!}\left[\:{cos}\left({x}\right)\ast\left({sin}\left({x}\right)\right)^{{n}+\mathrm{1}} \ast\left[\left({sin}\left({x}\right)\right)^{\mathrm{2}} \right]^{\left(\frac{−{n}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}\right)} \ast\:\mathrm{2}{F}_{\mathrm{1}} \left[\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{1}−{n}}{\mathrm{2}};\frac{\mathrm{3}}{\mathrm{2}};\left({cos}\left({x}\right)\right)^{\mathrm{2}} \right]\:\right]+{c} \\ $$$$ \\…
Question Number 22247 by tapan das last updated on 14/Oct/17 $$\mathrm{I}=\int\sqrt{}\mathrm{x}^{\mathrm{2}} +\mathrm{a}^{\mathrm{2}} \:\mathrm{dx} \\ $$ Answered by $@ty@m last updated on 14/Oct/17 Terms of Service…
Question Number 87769 by john santu last updated on 06/Apr/20 $$\int\:\frac{\mathrm{ln}\left(\mathrm{e}^{\mathrm{x}} +\mathrm{1}\right)}{\mathrm{e}^{−\mathrm{x}} +\mathrm{1}}\:\mathrm{dx}\: \\ $$ Answered by TANMAY PANACEA. last updated on 06/Apr/20 $$\int\frac{{e}^{{x}} {ln}\left({e}^{{x}}…
Question Number 22221 by Sahib singh last updated on 13/Oct/17 $$\int\:\:\frac{{a}_{\mathrm{0}} +{b}_{\mathrm{0}} {x}^{\mathrm{2}} }{\left({a}+{x}\right)^{\mathrm{2}} }{dx} \\ $$ Commented by Sahib singh last updated on 16/Oct/17…
Question Number 87757 by john santu last updated on 06/Apr/20 $$\int_{\mathrm{a}} ^{\mathrm{b}} \:\frac{\sqrt{\mathrm{x}−\mathrm{a}}}{\:\sqrt{\mathrm{b}−\mathrm{x}}}\:\mathrm{dx}\:=?\: \\ $$ Commented by john santu last updated on 06/Apr/20 $$\left.\mathrm{let}\:\mathrm{x}\:=\:\mathrm{a}\:+\:\left(\mathrm{b}−\mathrm{a}\right)\:\mathrm{w}\:\right] \\…
Question Number 22210 by cmaxamuud98 @gmail.com last updated on 13/Oct/17 $$\int\frac{\mathrm{4}{x}}{{e}^{\mathrm{3}{x}} }{dx} \\ $$ Answered by ajfour last updated on 13/Oct/17 $$=\mathrm{4}\int{xe}^{−\mathrm{3}{x}} {dx} \\ $$$$=\mathrm{4}\left\{{x}\int{e}^{−\mathrm{3}{x}}…
Question Number 87716 by Power last updated on 05/Apr/20 Commented by malwaan last updated on 05/Apr/20 $${put}\:{x}=\mathrm{2}{sin}\:{y}\:\Rightarrow\:{dx}=\mathrm{2}{cosydy} \\ $$$$\mathrm{3}{x}−{x}^{\mathrm{3}} \:=\:\mathrm{2}{sin}\mathrm{3}{y} \\ $$$$\therefore\:\int\:^{\mathrm{3}} \sqrt{\mathrm{2}{sin}\mathrm{3}{y}}\:.\:\mathrm{2}{cosy}\:{dy}\:=\:?? \\ $$…
Question Number 87723 by Ar Brandon last updated on 05/Apr/20 $$\int\left(\frac{\mathrm{1}}{{x}−\mathrm{1}}+\frac{\underset{{k}=\mathrm{0}} {\overset{\mathrm{2018}} {\sum}}\left({k}+\mathrm{1}\right){x}^{{k}} }{\underset{{k}=\mathrm{0}} {\overset{\mathrm{2019}} {\sum}}{x}^{{k}} }\right){dx} \\ $$ Answered by mahdi last updated on…
Question Number 87711 by M±th+et£s last updated on 05/Apr/20 $$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}−{xe}^{−{x}} −{e}^{−{x}} }{{x}\left({e}^{{x}} −{e}^{−{x}} \right)}{dx} \\ $$ Commented by mind is power last updated…
Question Number 22166 by Joel577 last updated on 12/Oct/17 $$\mathrm{If}\underset{\mathrm{1}} {\overset{\mathrm{4}} {\int}}\:{f}\left({x}\right)\:{dx}\:=\:\mathrm{5} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:{f}\left(\mathrm{3}{x}\:+\mathrm{1}\right)\:{dx}\:? \\ $$ Answered by ajfour last updated on 12/Oct/17…