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…
Question Number 137933 by mnjuly1970 last updated on 08/Apr/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 72398 by 20190927 last updated on 28/Oct/19 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left[\mathrm{x}−\mathrm{x}^{\mathrm{2}} \mathrm{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}\right)\right] \\ $$ Commented by mathmax by abdo last updated on 28/Oct/19 $${let}\:{f}\left({x}\right)={x}−{x}^{\mathrm{2}} {ln}\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)\:\:{we}\:{have}\:{ln}^{'}…
Question Number 72396 by mathmax by abdo last updated on 28/Oct/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{1}+{x}^{\mathrm{2}} }{\mathrm{2}+{x}^{\mathrm{2}} \:+{x}^{\mathrm{4}} }{dx} \\ $$ Commented by mathmax by abdo last…
Question Number 6861 by Tawakalitu. last updated on 31/Jul/16 $${Solve}\:{the}\:{partial}\:{fraction}\: \\ $$$$\frac{\mathrm{4}{s}^{\mathrm{3}} \:−\:\frac{\mathrm{39}}{\mathrm{2}}{s}^{\mathrm{2}} \:+\:\mathrm{42}{s}\:−\:\mathrm{40}}{{s}\left({s}\:−\:\mathrm{2}\right)\left({s}^{\mathrm{2}} \:−\:\mathrm{6}{s}\:+\:\mathrm{10}\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 72397 by mathmax by abdo last updated on 28/Oct/19 $${find}\:{A}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}−{xsin}^{\mathrm{2}} \theta\right){d}\theta\:\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$ Commented by mathmax by abdo last updated on…