Question Number 87881 by Rio Michael last updated on 06/Apr/20 $$\:\int_{−\infty} ^{\:+\infty} \frac{\mathrm{1}}{{x}}\:{dx}\:=\: \\ $$ Commented by mathmax by abdo last updated on 06/Apr/20 $${the}\:{function}\:{x}\rightarrow\frac{\mathrm{1}}{{x}}\:{is}\:{odd}\:\Rightarrow\int_{−\infty}…
Question Number 87876 by M±th+et£s last updated on 06/Apr/20 $${prove}\:{that} \\ $$$$\Gamma\left({z}\right)=\int_{\mathrm{0}} ^{\infty} {e}^{−{x}} \:{x}^{{z}−\mathrm{1}} \:{dx},{Re}\left({z}\right)>\mathrm{0} \\ $$ Commented by Joel578 last updated on 07/Apr/20…
Question Number 87854 by jagoll last updated on 06/Apr/20 $$\int\:\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{x}+\mathrm{2cos}\:\mathrm{x}+\mathrm{3}}\:\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated on 06/Apr/20 $${I}\:=\int\:\:\frac{{dx}}{\mathrm{2}{cosx}\:+{sinx}\:+\mathrm{3}}\:{we}\:{do}\:{the}\:{changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:\Rightarrow \\ $$$${I}\:=\int\:\:\:\frac{\mathrm{2}{dt}}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)\left(\mathrm{2}\frac{\mathrm{1}−{t}^{\mathrm{2}}…
Question Number 87839 by jagoll last updated on 06/Apr/20 $$\mathrm{I}\:=\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{4}}} {\int}}\:\frac{\mathrm{sin}\:\mathrm{4x}}{\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\sqrt{\mathrm{tan}\:^{\mathrm{4}} \mathrm{x}+\mathrm{1}}}\:\mathrm{dx} \\ $$ Answered by redmiiuser last updated on 06/Apr/20 $$\sqrt{\mathrm{tan}\:^{\mathrm{4}} {x}+\mathrm{1}}…
Question Number 87815 by jagoll last updated on 06/Apr/20 $$\mathrm{I}\:=\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\mathrm{cos}\:\mathrm{2x}\left(\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}+\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}\right)\:\mathrm{dx} \\ $$ Commented by john santu last updated on 06/Apr/20 $$\mathrm{cos}\:^{\mathrm{4}}…
Question Number 22261 by tapan das last updated on 14/Oct/17 $$\mathrm{Slove} \\ $$$$\int\mathrm{xtanx}\:\mathrm{dx} \\ $$ Answered by scottfeed last updated on 13/Nov/17 $${using}\:{integration}\:{by}\:{part}\:{formula}\:{to}\:{solve} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\int{udv}={uv}−\int{vdu}…
Question Number 87793 by M±th+et£s last updated on 06/Apr/20 $${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…