Question Number 11150 by suci last updated on 14/Mar/17 $${f}\left({x}\right)=\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{{sin}\mathrm{2}{x}} \\ $$$${f}'\left({x}\right)=…??? \\ $$ Answered by ajfour last updated on 14/Mar/17 $$=\:\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{sin}\:\mathrm{2}{x}} \:\left\{\left(\mathrm{2cos}\:\mathrm{2}{x}\right)\mathrm{ln}\:\left({x}^{\mathrm{2}}…
Question Number 11149 by suci last updated on 14/Mar/17 $$\int{x}^{\mathrm{5}} \:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +\mathrm{1}}\:{dx}=…??? \\ $$ Answered by ajfour last updated on 14/Mar/17 $$\:\frac{\left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{7}/\mathrm{3}} }{\mathrm{7}}−\frac{\left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{4}/\mathrm{3}}…
Question Number 11148 by suci last updated on 14/Mar/17 $$\int\frac{{x}\:{dx}}{\:\sqrt[{\mathrm{3}}]{{x}+\mathrm{1}}}=….??? \\ $$ Answered by ajfour last updated on 14/Mar/17 $$=\:\frac{\mathrm{3}\left({x}+\mathrm{1}\right)^{\mathrm{5}/\mathrm{3}} }{\mathrm{5}}\:−\frac{\mathrm{3}\left({x}+\mathrm{1}\right)^{\mathrm{2}/\mathrm{3}} }{\mathrm{2}}\:+{C}\: \\ $$ Commented…
Question Number 11147 by suci last updated on 14/Mar/17 $$\int{cos}^{\mathrm{4}} {x}\:{sinx}\:{dx}=….??? \\ $$ Answered by ajfour last updated on 14/Mar/17 $$=\:−\frac{\mathrm{cos}\:^{\mathrm{5}} {x}}{\mathrm{5}}+{C}\: \\ $$ Commented…
Question Number 11146 by suci last updated on 14/Mar/17 $$\int{sin}^{\mathrm{3}} \left(\mathrm{1}+\mathrm{2}{x}\right){dx}=….??? \\ $$ Answered by ajfour last updated on 14/Mar/17 $$=\:−\frac{\mathrm{3}}{\mathrm{8}}\mathrm{cos}\:\left(\mathrm{2}{x}+\mathrm{1}\right)+\frac{\mathrm{1}}{\mathrm{24}}\mathrm{cos}\:\left(\mathrm{6}{x}+\mathrm{3}\right)+{C} \\ $$ Commented by…
Question Number 76680 by Tony Lin last updated on 29/Dec/19 $${prove}\:{that}: \\ $$$$\:\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{7}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} {dx}=\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{3}} \right)^{\frac{\mathrm{1}}{\mathrm{7}}} {dx} \\ $$ Commented by…
Question Number 11145 by FilupS last updated on 14/Mar/17 $$\mathrm{let}\:\mathrm{set}\:{S}=\mathbb{R} \\ $$$$\mathrm{let}\:{nS}=\left\{\underset{{n}\:\mathrm{sets}\:\mathrm{of}\:\mathbb{R}} {\mathbb{R},\:\mathbb{R},\:…,\:\mathbb{R}}\right\}\:\:\:\:\:\:\:\:\:{n}\in\mathbb{Z}^{+} \\ $$$$\mathrm{is}\:\mid{S}\mid<\mid{nS}\mid? \\ $$$$\: \\ $$$$\mathrm{what}\:\mathrm{if}\:{n}=\mid{S}\mid? \\ $$ Commented by prakash jain…
Question Number 142218 by Dwaipayan Shikari last updated on 27/May/21 $${Straight}\:{line}\:{lx}+{my}=\mathrm{1}\:\:{is}\:{tangent}\:{to}\:{the}\:{curve}\:\left({ax}\right)^{{n}} +\left({by}\right)^{{n}} =\mathrm{1} \\ $$$${Prove}\:{that}\:\left(\frac{{l}}{{a}}\right)^{\frac{{n}}{{n}−\mathrm{1}}} +\left(\frac{{m}}{{b}}\right)^{\frac{{n}}{{n}−\mathrm{1}}} =\mathrm{1} \\ $$ Answered by som(math1967) last updated on…
Question Number 142212 by Rexzie last updated on 27/May/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 11139 by Joel576 last updated on 13/Mar/17 Commented by Joel576 last updated on 13/Mar/17 $$\mathrm{A}\:\mathrm{real}\:\mathrm{number}\:{t},\:\mathrm{so}\:\mathrm{there}\:\mathrm{is}\:\mathrm{a}\:\mathrm{three}−\mathrm{ordered}−\mathrm{pair} \\ $$$$\mathrm{solution}\:\left\{{x},\:{y},\:{z}\right\}\:\mathrm{that}\:\mathrm{fulfilled} \\ $$$${x}^{\mathrm{2}\:} \:+\:\mathrm{2}{y}^{\mathrm{2}} \:=\:\mathrm{3}{z}\:\:\:\mathrm{and}\:\:\:{x}\:+\:{y}\:+\:{z}\:=\:{t} \\ $$$$\mathrm{Find}\:{t}…