Question Number 137941 by Ñï= last updated on 08/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{{x}−\mathrm{1}}{\:\sqrt{\mathrm{2}^{{x}} −\mathrm{1}}{ln}\:\left(\mathrm{2}^{{x}} −\mathrm{1}\right)}{dx}=\frac{\pi}{\mathrm{2}{ln}^{\mathrm{2}} \mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 137940 by benjo_mathlover last updated on 08/Apr/21 $$\int_{\mathrm{1}} ^{\:{e}} \sqrt{\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }+\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}\:} }}\:{dx}\:=? \\ $$ Answered by john_santu last updated on 08/Apr/21 $$\mathcal{J}\:=\:\int_{\mathrm{1}} ^{\:{e}}…
Question Number 6870 by Tawakalitu. last updated on 31/Jul/16 $${Solve}\:{for}\:{x}\:{in}\: \\ $$$$ \\ $$$$\mathrm{4}^{{x}} \:=\:\frac{\mathrm{192}}{{x}} \\ $$$$ \\ $$$${Using}\:{lambert}\:{function}\: \\ $$ Commented by Yozzii last…
Question Number 137943 by john_santu last updated on 08/Apr/21 $${Determine}\:{the}\:{term}\:{independent} \\ $$$${of}\:{x}\:{in}\:{the}\:{expansion}\: \\ $$$$\:\:\:\:\left(\frac{{x}+\mathrm{1}}{{x}^{\mathrm{2}/\mathrm{3}} −{x}^{\mathrm{1}/\mathrm{3}} +\mathrm{1}}\:−\frac{{x}−\mathrm{1}}{{x}−{x}^{\mathrm{1}/\mathrm{2}} }\:\right)^{\mathrm{10}} \:. \\ $$ Answered by EDWIN88 last updated…
Question Number 137937 by benjo_mathlover last updated on 08/Apr/21 $$\:\underset{−\infty} {\overset{\:\:\:\infty} {\int}}\frac{\mathrm{ln}\left(\:\mid{x}\mid\right)}{\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:=? \\ $$ Answered by Ñï= last updated on 14/Apr/21 $$\int_{−\infty}…
Question Number 137936 by Ñï= last updated on 08/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\begin{pmatrix}{\mathrm{4}{n}}\\{\mathrm{2}{n}}\end{pmatrix}^{−\mathrm{1}} =\frac{\mathrm{16}}{\mathrm{15}}+\frac{\sqrt{\mathrm{3}}}{\mathrm{27}}\pi−\frac{\mathrm{2}\sqrt{\mathrm{5}}}{\mathrm{25}}{ln}\left(\mathrm{1}+\frac{\sqrt{\mathrm{5}}}{\mathrm{2}}\right) \\ $$ Commented by Dwaipayan Shikari last updated on 08/Apr/21 $$\underset{{n}=\mathrm{0}} {\overset{\infty}…
Question Number 137939 by Ñï= last updated on 08/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} {ln}\Gamma\left(\mathrm{1}+{x}+{y}\right){dxdy}=\frac{\mathrm{5}}{\mathrm{2}}{ln}\mathrm{2}+\frac{\mathrm{1}}{\mathrm{2}}{ln}\pi−\frac{\mathrm{9}}{\mathrm{4}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 6865 by Tawakalitu. last updated on 31/Jul/16 $$\int\frac{{sin}\left({x}\right)\:+\:{cos}\left({x}\right)}{{e}^{−{x}} \:+\:{sin}\left({x}\right)}\:{dx} \\ $$ Commented by Yozzii last updated on 31/Jul/16 $${sinhix}={isinx} \\ $$$${sinx}=\frac{{sinhix}}{{i}}=\frac{{e}^{{ix}} −{e}^{−{ix}} }{\mathrm{2}{i}}…
Question Number 137938 by Ñï= last updated on 09/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{\mathrm{2}{x}^{\mathrm{4}} +\mathrm{5}{x}^{\mathrm{3}} +\mathrm{6}{x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{12}}{\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}\right)^{\mathrm{3}/\mathrm{2}} }{dx}=? \\ $$$${A}\:{very}\:{nice}\:{solution}:: \\ $$$$\int\frac{\mathrm{2}{x}^{\mathrm{4}} +\mathrm{5}{x}^{\mathrm{3}} +\mathrm{6}{x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{12}}{\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}\right)^{\mathrm{3}/\mathrm{2}} }{dx}=\frac{{f}\left({x}\right)}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}}}+{C}…
Question Number 72401 by Learner-123 last updated on 28/Oct/19 $${Find}\:{the}\:{area}\:{bounded}\:{by}\:{one}\:{leaf}\:{of} \\ $$$${the}\:{rose}\:{r}\:=\:\mathrm{12cos}\:\left(\mathrm{3}\theta\right). \\ $$ Answered by ajfour last updated on 28/Oct/19 Commented by ajfour last…