Question Number 133872 by MJS_new last updated on 24/Feb/21 $$\int\frac{{dx}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)\sqrt{{x}^{\mathrm{4}} −\mathrm{1}}}=? \\ $$ Commented by MJS_new last updated on 24/Feb/21 $$\mathrm{I}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{it}\:\mathrm{but}\:\mathrm{maybe}\:\mathrm{there}'\mathrm{s}\:\mathrm{an}\:\mathrm{easier}\:\mathrm{path}… \\ $$ Commented…
Question Number 68316 by 9102176137086 last updated on 08/Sep/19 $$\int\left(\mathrm{4sin}\:\mathrm{3}{x}+\frac{{e}^{\mathrm{4}{x}} }{\mathrm{4}}\right) \\ $$ Commented by mathmax by abdo last updated on 08/Sep/19 $$=\mathrm{4}\int\:{sin}\left(\mathrm{3}{x}\right){dx}\:+\frac{\mathrm{1}}{\mathrm{4}}\int\:{e}^{\mathrm{4}{x}} {dx}\:+{c} \\…
Question Number 68313 by 9102176137086 last updated on 08/Sep/19 $$\int\left(\mathrm{1}−\frac{\mathrm{6}}{{x}}+\frac{\mathrm{2}}{{x}^{\mathrm{2}} }+\sqrt{{x}}\right) \\ $$ Commented by mathmax by abdo last updated on 10/Sep/19 $$\int\:\left(\mathrm{1}−\frac{\mathrm{6}}{{x}}+\frac{\mathrm{2}}{{x}^{\mathrm{2}} }\:+\sqrt{{x}}\right){dx}\:={x}−\mathrm{6}{ln}\mid{x}\mid\:+\frac{\mathrm{2}}{\mathrm{3}}{x}^{\frac{\mathrm{3}}{\mathrm{2}\:}} \:+{c}…
Question Number 2770 by Yozzi last updated on 26/Nov/15 $$\int_{\mathrm{2}} ^{\infty} \frac{{dx}}{{x}\sqrt{{x}−\mathrm{1}}}=? \\ $$ Answered by prakash jain last updated on 27/Nov/15 $${x}−\mathrm{1}=\mathrm{tan}^{\mathrm{2}} {u} \\…
Question Number 133825 by mnjuly1970 last updated on 24/Feb/21 Answered by mathDivergent last updated on 24/Feb/21 $$\frac{\mathrm{1}}{\mathrm{4}}\zeta\left(\mathrm{3}\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 2751 by prakash jain last updated on 26/Nov/15 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\:{i}}{{i}}=\frac{\pi}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by prakash jain last updated on 27/Nov/15…
Question Number 68271 by ~ À ® @ 237 ~ last updated on 08/Sep/19 $$\:\:{Find}\:\:{J}=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{W}\left(−{ulnu}\right)}{{ulnu}}\:{du}\:\:\:\:{when}\:\:{W}\:{is}\:{the}\:{lambert}\:{function} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 133791 by mnjuly1970 last updated on 24/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:……{advanced}\:\:\:\:{integral}…. \\ $$$$\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \left(\frac{\mathrm{1}−{e}^{−\varphi{x}} }{\mathrm{1}+{e}^{\varphi{x}} }\:\right)\frac{{dx}}{{x}}\:=?? \\ $$$$\:\:\:\varphi:\:=\:{Golden}\:{ratio}… \\ $$$$ \\ $$ Answered…
Question Number 133786 by bobhans last updated on 24/Feb/21 $$\mathcal{A}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \mathrm{sin}^{−\mathrm{1}} \left(\frac{{x}^{\mathrm{2}} +\mathrm{1}}{\:\sqrt{\mathrm{2}{x}^{\mathrm{4}} +\mathrm{2}}}\:\right)\:{dx}\:=? \\ $$ Answered by john_santu last updated on 24/Feb/21 $${Using}\:{the}\:{Pythagorean}\:{theorem}\:…
Question Number 68241 by mathmax by abdo last updated on 07/Sep/19 $${calculate}\:\int\int_{{w}} \:\:\:\left({x}^{\mathrm{2}} −\mathrm{2}{y}^{\mathrm{2}} \right)\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} }{dxdy} \\ $$$${with}\:{w}\:=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:\:{and}\:\mathrm{1}\leqslant{y}\leqslant\mathrm{2}\right\} \\ $$ Commented by mathmax…