Question Number 57494 by bshahid010@gmail.com last updated on 05/Apr/19 Commented by MJS last updated on 06/Apr/19 $$\mathrm{11}^{\mathrm{cos}\:{x}\:−\mathrm{sin}\:{x}} =\mathrm{11}^{\sqrt{\mathrm{2}}\mathrm{cos}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)} \\ $$$$\mathrm{11}^{\mathrm{sin}\:{x}\:−\mathrm{cos}\:{x}} =\mathrm{11}^{−\sqrt{\mathrm{2}}\mathrm{cos}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)} \\ $$$$\sqrt{\mathrm{2}}\left(\mathrm{cos}\:{x}\:+\mathrm{sin}\:{x}\right)=\mathrm{2sin}\:\left({x}+\frac{\pi}{\mathrm{4}}\right) \\ $$$$\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{the}\:\mathrm{1}^{\mathrm{st}}…
Question Number 188560 by 073 last updated on 03/Mar/23 Answered by Rasheed.Sindhi last updated on 03/Mar/23 $${Let}\:{P}\left({x}\right)={ax}+{b} \\ $$$${P}\left(\mathrm{2}{x}\right)={a}\left(\mathrm{2}{x}\right)+{b}=\mathrm{2}{ax}+{b} \\ $$$${P}\left({x}\right)+{P}\left(\mathrm{2}{x}\right)=\mathrm{6}{x}+\mathrm{12} \\ $$$$\left({ax}+{b}\right)+\left(\mathrm{2}{ax}+{b}\right)=\mathrm{6}{x}+\mathrm{12} \\ $$$$\mathrm{3}{ax}+\mathrm{2}{b}=\mathrm{6}{x}+\mathrm{12}…
Question Number 188557 by MathsFan last updated on 03/Mar/23 $$\int\sqrt{\boldsymbol{{x}}\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{1}}}\boldsymbol{{dx}} \\ $$ Answered by MJS_new last updated on 03/Mar/23 $$\int{x}^{\mathrm{1}/\mathrm{2}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{1}/\mathrm{4}} {dx}= \\…
Question Number 188545 by 073 last updated on 03/Mar/23 Answered by ARUNG_Brandon_MBU last updated on 03/Mar/23 $$\int\left(\frac{\mathrm{1}}{\mathrm{sin}\frac{{x}}{\:\sqrt{\mathrm{2}}}}−\mathrm{2}+\mathrm{sin}\frac{{x}}{\:\sqrt{\mathrm{2}}}\right){dx} \\ $$$$=\sqrt{\mathrm{2}}\mathrm{ln}\mid\mathrm{cosec}\frac{{x}}{\:\sqrt{\mathrm{2}}}−\mathrm{cot}\frac{{x}}{\:\sqrt{\mathrm{2}}}\mid−\mathrm{2}{x}−\sqrt{\mathrm{2}}\mathrm{cos}\frac{{x}}{\:\sqrt{\mathrm{2}}}+{C} \\ $$ Terms of Service Privacy…
Question Number 188544 by 073 last updated on 03/Mar/23 Answered by ARUNG_Brandon_MBU last updated on 03/Mar/23 $$\int\frac{{e}^{\mathrm{arctan}{x}} }{\mathrm{1}+{x}^{\mathrm{2}} }{dx}+\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}{x}\mathrm{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}+\int\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$={e}^{\mathrm{arctan}{x}} +\frac{\mathrm{ln}^{\mathrm{2}}…
Question Number 123007 by mohammad17 last updated on 21/Nov/20 Commented by mohammad17 last updated on 21/Nov/20 $${how}\:{can}\:{solve}\:{it}\:? \\ $$ Commented by mr W last updated…
Question Number 123009 by aurpeyz last updated on 21/Nov/20 Commented by aurpeyz last updated on 21/Nov/20 $${pls}\:{help}\:{with}\:{question}\:\mathrm{1} \\ $$ Answered by Dwaipayan Shikari last updated…
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Question Number 123005 by mohammad17 last updated on 21/Nov/20 Commented by mohammad17 last updated on 21/Nov/20 $${please}\:{sir}\:{help}\:{me}\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 122999 by ZiYangLee last updated on 21/Nov/20 $${A}_{\mathrm{1}} ,{A}_{\mathrm{2}} ,{A}_{\mathrm{3}} ,\ldots,{A}_{{n}} \:\mathrm{are}\:\mathrm{defined}\:\mathrm{as}\:\mathrm{follows} \\ $$$$\:\:\:\:{A}_{\mathrm{1}} =\mathrm{2},\:{A}_{{n}−\mathrm{1}} =\mathrm{2}\left({A}_{\mathrm{1}} +{A}_{\mathrm{2}} +{A}_{\mathrm{3}} +\ldots+{A}_{{n}} \right) \\ $$$${for}\:{n}=\mathrm{1},\mathrm{2},\mathrm{3},\ldots \\…