Question Number 150037 by RoswelCod2003 last updated on 09/Aug/21 $${Random}\:{Problem}: \\ $$$$\underset{\frac{\pi}{\mathrm{4}}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\left(−\mathrm{7sin}\:{x}\:+\:\mathrm{3cos}\:{x}\right)\:{dx} \\ $$$$ \\ $$$${By}\:{getting}\:{the}\:{antiderivative}\:{of}\:{the}\:{trigonometric}\:{functions}: \\ $$$$\int\:\mathrm{sin}\left({x}\right)\:{dx}\:=\:−\mathrm{cos}\:{x}\:+\:{c} \\ $$$$\int\:\mathrm{cos}\left({x}\right)\:{dx}\:=\:\mathrm{sin}\:{x}\:+\:{c} \\ $$$$=\:−\mathrm{7}\:\int\:\mathrm{sin}\:{x}\:\:+\:\:\mathrm{3}\:\int\:\mathrm{cos}\:{x}\:\underset{\frac{\pi}{\mathrm{4}}} {\overset{\frac{\pi}{\mathrm{2}}}…
Question Number 84498 by M±th+et£s last updated on 13/Mar/20 $$\int\sqrt{{x}}\:{cos}\sqrt{{x}}\:{dx} \\ $$ Commented by jagoll last updated on 13/Mar/20 $$\int\:\frac{{x}\:\mathrm{cos}\:\sqrt{{x}}}{\:\sqrt{{x}}}\:{dx}\: \\ $$$${let}\:\sqrt{{x}}\:=\:{t}\:\Rightarrow\:{x}={t}^{\mathrm{2}} \\ $$$${dx}\:=\:\mathrm{2}{t}\:{dt} \\…
Question Number 84497 by M±th+et£s last updated on 13/Mar/20 $$\int\frac{{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{5}} }\:{dx} \\ $$$$ \\ $$ Commented by mathmax by abdo last updated on 13/Mar/20…
Question Number 84467 by jagoll last updated on 13/Mar/20 $$\int\:\mathrm{ln}\left(\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)\right)\:\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 84456 by M±th+et£s last updated on 13/Mar/20 $${y}={ln}\sqrt{\frac{{a}+{sin}\left({x}\right)}{{b}−{sin}\left({x}\right)}} \\ $$$${if}\:\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} −{tan}^{\mathrm{2}} \left({x}\right)=\mathrm{1} \\ $$$${show}\:{that}\:{a}={b} \\ $$ Commented by jagoll last updated on 13/Mar/20…
Question Number 149986 by mnjuly1970 last updated on 08/Aug/21 Answered by mindispower last updated on 08/Aug/21 $${ln}\left(\mathrm{1}+{e}^{{x}} \right)={x}+{ln}\left({e}^{−{x}} +\mathrm{1}\right) \\ $$$${I}=\int_{\mathrm{0}} ^{\infty} \frac{{x}}{\mathrm{1}+{e}^{\mathrm{2}{x}} }{dx}+\int_{\mathrm{0}} ^{\infty}…
Question Number 84446 by Power last updated on 13/Mar/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 18889 by Joel577 last updated on 01/Aug/17 $$\int\:\frac{{d}\left(\sqrt{\mathrm{3}{x}}\right)}{\:\sqrt{\sqrt{{x}}\:+\:\mathrm{7}}} \\ $$ Commented by Joel577 last updated on 01/Aug/17 $$\mathrm{I}\:\mathrm{got}\:\mathrm{2}\sqrt{\mathrm{3}\left(\sqrt{{x}}\:+\:\mathrm{7}\right)}\:+\:{C} \\ $$$$\mathrm{is}\:\mathrm{it}\:\mathrm{correct}? \\ $$ Commented…
Question Number 149944 by ArielVyny last updated on 08/Aug/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{t}^{\frac{{n}−\mathrm{1}}{\mathrm{2}}} }{\left(\mathrm{1}+{t}\right)^{{n}+\mathrm{1}} }{dt} \\ $$ Commented by Ar Brandon last updated on 08/Aug/21 $$\beta\left(\mathrm{m},\:\mathrm{n}\right)=\int_{\mathrm{0}}…
Question Number 84415 by TawaTawa1 last updated on 12/Mar/20 $$\int\:\sqrt{\mathrm{x}\:−\:\sqrt{\mathrm{4}\:−\:\mathrm{x}^{\mathrm{2}} }}\:\:\mathrm{dx} \\ $$ Answered by john santu last updated on 13/Mar/20 $$\mathrm{let}\:\mathrm{x}\:=\:\mathrm{2sin}\:\mathrm{t} \\ $$$$\int\:\sqrt{\mathrm{2sin}\:\mathrm{t}−\mathrm{2cos}\:\mathrm{t}}\:×\mathrm{2cos}\:\mathrm{t}\:\mathrm{dt} \\…