Question Number 53382 by gunawan last updated on 21/Jan/19 $$\int\:\mathrm{cos}^{\mathrm{3}} {x}\:{e}^{\mathrm{log}\:\left(\mathrm{sin}\:{x}\right)} {dx}\:= \\ $$ Answered by math1967 last updated on 21/Jan/19 $$\int\left(\mathrm{1}−{sin}^{\mathrm{2}} {x}\right){cosxe}^{{ln}\left({sinx}\right)} {dx} \\…
Question Number 53381 by gunawan last updated on 21/Jan/19 $$\int\:\frac{\mathrm{1}}{\left[\left({x}−\mathrm{1}\right)^{\mathrm{3}} \left({x}+\mathrm{2}\right)^{\mathrm{5}} \right]^{\mathrm{1}/\mathrm{4}} }\:{dx}\:= \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 21/Jan/19 $$\int\frac{{dx}}{\left({x}−\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{4}}} \left({x}+\mathrm{2}\right)^{\frac{\mathrm{5}}{\mathrm{4}}} }…
Question Number 53359 by gunawan last updated on 20/Jan/19 $$\int\:\:\frac{{x}^{\mathrm{3}} −\mathrm{1}}{{x}^{\mathrm{3}} +{x}}\:{dx}\:= \\ $$ Answered by Smail last updated on 21/Jan/19 $${I}=\int\frac{{x}^{\mathrm{3}} +{x}−{x}−\mathrm{1}}{{x}^{\mathrm{3}} +{x}}{dx}=\int\left(\mathrm{1}−\frac{{x}+\mathrm{1}}{{x}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}\right){dx}…
Question Number 53358 by gunawan last updated on 20/Jan/19 $$\int\:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{sin}^{\mathrm{3}} {x}\:\mathrm{cos}\:{x}}}\:{dx}\:= \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 21/Jan/19 $$\int\frac{{dx}}{\:\sqrt{{sin}^{\mathrm{3}} {xcosx}}} \\ $$$$\int\frac{{dx}}{\:\sqrt{\frac{{sin}^{\mathrm{3}} {x}}{{cos}^{\mathrm{3}}…
Question Number 53357 by gunawan last updated on 20/Jan/19 $$\int\:\:\frac{\left({x}^{\mathrm{4}} −{x}\right)^{\mathrm{1}/\mathrm{4}} }{{x}^{\mathrm{5}} }\:{dx}\:= \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 21/Jan/19 $$\int\frac{\left\{{x}^{\mathrm{4}} \left(\mathrm{1}−\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\right)\right\}^{\frac{\mathrm{1}}{\mathrm{4}}}…
Question Number 53324 by 0955083339 last updated on 20/Jan/19 $$\mathrm{If}\:\mathrm{4}{a}\:+\:\mathrm{5}{b}\:+\:\mathrm{9}{c}=\mathrm{36}\:\mathrm{and}\:\mathrm{7}{a}\:+\:\mathrm{9}{b}\:+\:\mathrm{17}{c}=\mathrm{66}, \\ $$$$\mathrm{then}\:{a}+{b}+{c}=\_\_\_\_\_. \\ $$ Answered by Kunal12588 last updated on 21/Jan/19 $${let}\:{a}+{b}+{c}={k} \\ $$$$\mathrm{4}{a}+\mathrm{4}{b}+\mathrm{4}{c}+{b}+\mathrm{5}{c}=\mathrm{36} \\…
Question Number 53277 by 0955083339 last updated on 19/Jan/19 $$\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:\:\frac{{x}}{\left(\mathrm{1}−{x}\right)^{\mathrm{3}/\mathrm{4}} }\:{dx}\:= \\ $$ Commented by maxmathsup by imad last updated on 19/Jan/19 $${let}\:{I}\:=\int_{\mathrm{0}}…
Question Number 53141 by gunawan last updated on 18/Jan/19 $$\mathrm{If}\:{n}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integer}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{unity},\:\mathrm{then} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$${a}−\:^{{n}} {C}_{\mathrm{1}} \left({a}−\mathrm{1}\right)+\:^{{n}} {C}_{\mathrm{2}} \left({a}−\mathrm{2}\right)−\:^{{n}} {C}_{\mathrm{3}} \left({a}−\mathrm{3}\right)+… \\ $$$$\:\:\:\:\:\:\:..+\left(−\mathrm{1}\right)^{{n}} \left({a}−{n}\right)\:\mathrm{is} \\ $$…
Question Number 52950 by gunawan last updated on 15/Jan/19 $$\:\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{3}+\mathrm{sin}\:\mathrm{2}{x}}\:{dx}\:= \\ $$ Commented by maxmathsup by imad last updated on 15/Jan/19 $${let}\:{A}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}}…
Question Number 52949 by gunawan last updated on 15/Jan/19 $$\mathrm{If}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{an}\:\mathrm{odd}\:\mathrm{function},\:\mathrm{then} \\ $$$$\underset{\:\mathrm{0}} {\overset{\pi} {\int}}\:{f}\:\left(\mathrm{cos}\:{x}\right)\:{dx}\:=\:\mathrm{2}\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:{f}\:\left(\mathrm{cos}\:{x}\right)\:{dx} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 15/Jan/19…