যোজিত ফল নির্ণয় কর : $\int_{0}^{1} \frac{x e^{x}}{{(1 + x)}^{2}}$

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

এখন, $\int_{0}^{1} \frac{{xe}^{x}}{{(1 + x)}^{2}}$

$= e^{x} \{\frac{1}{(1 + x)} + \frac{(- 1)}{{(1 + x)}^{2}}\} = e^{x} / (1 + x)$

$∴ \int_{0}^{1} \frac{e^{x} x}{{(1 + x)}^{2}} = {[\frac{e^{x}}{(1 + x)}]}_{0}^{1}$

$= (\frac{e}{2} - \frac{e^{\circ}}{1}) = \frac{e}{2} - 1 (A n s)$

1 year ago

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