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0-e-x-3-1-1-x-3-3-dx-x-1-3-1-3-

Question Number 138619 by Dwaipayan Shikari last updated on 15/Apr/21 $$\int_{\mathrm{0}} ^{\infty} \left({e}^{−{x}^{\sqrt{\mathrm{3}}} } −\frac{\mathrm{1}}{\left(\mathrm{1}+{x}^{\sqrt{\mathrm{3}}} \right)^{\sqrt{\mathrm{3}}} }\right)\frac{{dx}}{{x}}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\psi\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\right) \\ $$ Commented by mnjuly1970 last updated on…

Prove-or-disprove-0-a-x-2-e-x-2-dx-1-e-a-2-a-3-1-3-2a-5-1-3-5-2a-7-1-3-5-7-2a-9-1-3-5-7-9-ad-inf-

Question Number 138608 by Dwaipayan Shikari last updated on 15/Apr/21 $${Prove}\:{or}\:{disprove} \\ $$$$\int_{\mathrm{0}} ^{{a}} {x}^{\mathrm{2}} {e}^{−{x}^{\mathrm{2}} } {dx}=\frac{\mathrm{1}}{{e}^{{a}^{\mathrm{2}} } }\left(\frac{{a}^{\mathrm{3}} }{\mathrm{1}.\mathrm{3}}+\frac{\mathrm{2}{a}^{\mathrm{5}} }{\mathrm{1}.\mathrm{3}.\mathrm{5}}+\frac{\mathrm{2}{a}^{\mathrm{7}} }{\mathrm{1}.\mathrm{3}.\mathrm{5}.\mathrm{7}}+\frac{\mathrm{2}{a}^{\mathrm{9}} }{\mathrm{1}.\mathrm{3}.\mathrm{5}.\mathrm{7}.\mathrm{9}}+{ad}\:{inf}..\right) \\…

Question-73030

Question Number 73030 by Tanmay chaudhury last updated on 05/Nov/19 Answered by Tanmay chaudhury last updated on 05/Nov/19 $$\int_{\mathrm{0}} ^{\mathrm{4}} \frac{{ln}\mathrm{2}}{{lnx}}−\frac{{ln}\mathrm{2}×{ln}\mathrm{2}}{{lnx}×{lnx}×{ln}\mathrm{2}}{dx} \\ $$$${ln}\mathrm{2}\int_{\mathrm{2}} ^{\mathrm{4}} \frac{\mathrm{1}}{{lnx}}−\frac{\mathrm{1}}{\left({lnx}\right)^{\mathrm{2}}…

Produce-a-3-3-array-of-different-numbers-whose-all-the-rows-and-all-the-columns-make-AP-s-of-different-common-digfernces-

Question Number 7423 by Rasheed Soomro last updated on 28/Aug/16 $${Produce}\:{a}\:\mathrm{3}×\mathrm{3}\:\boldsymbol{{array}}\:{of}\:\boldsymbol{{different}}\:{numbers} \\ $$$${whose}\:{all}\:{the}\:\boldsymbol{{rows}}\:{and}\:{all}\:{the}\:\boldsymbol{{columns}}\:{make} \\ $$$$\boldsymbol{{AP}}'\boldsymbol{{s}}\:{of}\:\boldsymbol{{different}}\:\boldsymbol{{common}}-\boldsymbol{{digfernces}}. \\ $$ Commented by Yozzia last updated on 28/Aug/16 $$\begin{pmatrix}{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}\\{\mathrm{5}}&{\mathrm{7}}&{\mathrm{9}}\\{\mathrm{9}}&{\mathrm{12}}&{\mathrm{15}}\end{pmatrix}\:…