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Category: Integration

x-2-sinh-x-tan-1-x-log-x-4-1-pie-x-2-x-8-3cosh-x-1-3-dx-

Question Number 96911 by Ar Brandon last updated on 05/Jun/20 $$\int_{−\infty} ^{+\infty} \frac{\mathrm{x}^{\mathrm{2}} \mathrm{sinh}\left(\mathrm{x}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)\centerdot\mathrm{log}\left(\mathrm{x}^{\mathrm{4}} +\mathrm{1}\right)}{\pi\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } +\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{8}} +\mathrm{3cosh}\left(\mathrm{x}\right)}}\mathrm{dx} \\ $$ Commented by 675480065 last…

Question-96898

Question Number 96898 by bobhans last updated on 05/Jun/20 Commented by PRITHWISH SEN 2 last updated on 05/Jun/20 $$\frac{\mathrm{1}}{\mathrm{6}}\int\left\{\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{6x}}\:+\mathrm{x}\right\}\mathrm{dx}=\frac{\mathrm{1}}{\mathrm{6}}\int\sqrt{\left(\mathrm{x}+\mathrm{3}\right)^{\mathrm{2}} −\mathrm{9}}\:\mathrm{dx}\:+\frac{\mathrm{1}}{\mathrm{6}}\int\mathrm{xdx} \\ $$$$=\frac{\left(\mathrm{x}+\mathrm{3}\right)}{\mathrm{12}}\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{6x}}\:−\frac{\mathrm{3}}{\mathrm{4}}\mathrm{ln}\mid\left(\mathrm{x}+\mathrm{3}\right)+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{6x}}\mid+\frac{\mathrm{x}^{\mathrm{2}}…

Question-96846

Question Number 96846 by bobhans last updated on 05/Jun/20 Commented by john santu last updated on 05/Jun/20 $$\left[\:{a}^{\mathrm{2}} {x}+\left(\mathrm{2}−\mathrm{2}{a}\right){x}^{\mathrm{2}} +{x}^{\mathrm{4}} \:\right]_{\mathrm{1}} ^{\mathrm{2}} \:\leqslant\:\mathrm{12} \\ $$$$\Leftrightarrow\:{a}^{\mathrm{2}}…

1-calculate-I-n-0-dx-2x-2-5x-3-n-2-calculate-0-dx-2x-2-5x-3-2-and-0-dx-2x-2-5x-3-3-

Question Number 96834 by mathmax by abdo last updated on 05/Jun/20 $$\left.\mathrm{1}\right)\mathrm{calculate}\:\mathrm{I}_{\mathrm{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{dx}}{\left(\mathrm{2x}^{\mathrm{2}} +\mathrm{5x}+\mathrm{3}\right)^{\mathrm{n}} } \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{2x}^{\mathrm{2}} \:+\mathrm{5x}+\mathrm{3}\right)^{\mathrm{2}} }\:\mathrm{and}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{2x}^{\mathrm{2}}…