Question Number 84884 by bshahid010@gmail.com last updated on 17/Mar/20 Commented by mathmax by abdo last updated on 17/Mar/20 $${A}\:=\int\:\:\frac{{dx}}{\left(\mathrm{2}{x}−\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{3}}}\:{changement}\:\mathrm{2}{x}−\mathrm{1}={t}\:{give}\:{x}=\frac{{t}+\mathrm{1}}{\mathrm{2}} \\ $$$${A}\:=\int\:\:\frac{{dt}}{\mathrm{2}{t}\sqrt{\frac{\left({t}+\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{4}}+\frac{{t}+\mathrm{1}}{\mathrm{2}}+\mathrm{3}}}\:=\int\:\:\frac{{dt}}{\mathrm{2}{t}\sqrt{\frac{{t}^{\mathrm{2}} +\mathrm{2}{t}+\mathrm{1}+\mathrm{2}{t}+\mathrm{2}+\mathrm{12}}{\mathrm{4}}}} \\…
Question Number 150413 by saly last updated on 12/Aug/21 Commented by MJS_new last updated on 12/Aug/21 $$\mathrm{in}\:\mathrm{this}\:\mathrm{case}\:\mathrm{we}\:\mathrm{must}\:\mathrm{take}\:\mathrm{the}\:\mathrm{long}\:\mathrm{way}\:\mathrm{home}… \\ $$$$ \\ $$$$\left(\mathrm{1}\right)\:\mathrm{arctan}\:{r}\:=−\frac{\mathrm{i}}{\mathrm{2}}\left(\mathrm{ln}\:\left(\mathrm{1}+\mathrm{i}{r}\right)\:−\mathrm{ln}\:\left(\mathrm{1}−\mathrm{i}{r}\right)\right) \\ $$$$\Rightarrow \\ $$$$\int\mathrm{arctan}\:\mathrm{sin}\:{x}\:{dx}=…
Question Number 150372 by tabata last updated on 11/Aug/21 Commented by mathdanisur last updated on 11/Aug/21 $$\underset{{a}} {\overset{{a}+\mathrm{1}} {\int}}{f}\left({x}\right){dx}=\mathrm{2}\:\:\Rightarrow\underset{{a}} {\overset{{a}+\mathrm{1}} {\int}}\left(\frac{\mathrm{1}}{\mathrm{1}+{x}}\:+\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{3}} }\:+\:…\:+\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{{n}} }\right){dx}\:=\:\mathrm{2}\:\:\left(\mathrm{1}\right) \\…
Question Number 19294 by mondodotto@gmail.com last updated on 08/Aug/17 Answered by mrW1 last updated on 08/Aug/17 $$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2x}^{\mathrm{2}} +\mathrm{5x}+\mathrm{3} \\ $$$$=\mathrm{2}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2}×\frac{\mathrm{5}}{\mathrm{4}}\mathrm{x}+\frac{\mathrm{25}}{\mathrm{16}}\right)+\mathrm{3}−\frac{\mathrm{25}}{\mathrm{8}} \\ $$$$=\mathrm{2}\left(\mathrm{x}+\frac{\mathrm{5}}{\mathrm{4}}\right)^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{8}} \\…
Question Number 150362 by otchereabdullai@gmail.com last updated on 11/Aug/21 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{p}=\left(\mathrm{3i}+\mathrm{4j}\right)\:,\:\mathrm{q}=\left(\mathrm{2i}−\mathrm{j}\right)\:\mathrm{and} \\ $$$$\mathrm{r}=\mathrm{5i}−\mathrm{j}.\:\mathrm{Express}\:\:\mathrm{vector}\:\:\:\mathrm{r}\:\:\mathrm{intrems}\:\mathrm{of} \\ $$$$\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:. \\ $$ Answered by mr W last updated on 11/Aug/21 $${say}\:{r}={ap}+{bq}…
Question Number 150351 by eman_64 last updated on 11/Aug/21 Commented by eman_64 last updated on 11/Aug/21 $$\:\mathrm{How}\:\mathrm{do} \\ $$ Commented by mathdanisur last updated on…
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Question Number 19264 by mondodotto@gmail.com last updated on 08/Aug/17 Commented by Satyamtt last updated on 08/Aug/17 $$\mathrm{Is}\:\mathrm{it}\:\mathrm{23}\:?\:\left(\mathrm{by}\:\mathrm{method}\:\mathrm{of}\:\mathrm{differences}\right) \\ $$ Commented by RasheedSindhi last updated on…
Question Number 19268 by khamizan833@yahoo.com last updated on 08/Aug/17 Answered by ajfour last updated on 08/Aug/17 $$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}\left(\frac{\mathrm{1}}{\mathrm{1}−\mathrm{2}^{\mathrm{x}} }−\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$$$\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}\left(−\mathrm{x}\right)=\mathrm{x}\left[\left(\frac{\mathrm{1}}{\mathrm{1}−\mathrm{2}^{\mathrm{x}} }−\frac{\mathrm{1}}{\mathrm{2}}\right)−\left(\frac{\mathrm{2}^{\mathrm{x}} }{\mathrm{2}^{\mathrm{x}} −\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{2}}\right)\right] \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=−\frac{\left(\mathrm{2}^{\mathrm{x}}…
Question Number 150324 by lapache last updated on 11/Aug/21 $${Calcul}\:{des}\:{sommes} \\ $$$${A}−\:\:\underset{{p}=\mathrm{0}} {\overset{\alpha} {\sum}}{C}_{{n}} ^{\mathrm{2}{p}} =…..\:\:{avec}\:\:\alpha={E}\left(\frac{{n}}{\mathrm{2}}\right) \\ $$$${B}−\:\underset{{p}=\mathrm{0}} {\overset{\beta} {\sum}}{C}_{{n}} ^{\mathrm{2}{p}+\mathrm{1}} =…..\:\:{avec}\:\beta={E}\left(\frac{{n}−\mathrm{1}}{\mathrm{2}}\right) \\ $$ Terms…