Question Number 310 by 123456 last updated on 25/Jan/15 | ||
$$\underset{\mathrm{1}} {\overset{{e}} {\int}}{xe}^{{t}} −\frac{\mathrm{ln}\:{x}}{{x}}{dx} \\ $$ | ||
Answered by prakash jain last updated on 20/Dec/14 | ||
$$\int{xe}^{{t}} {dx}−\int\frac{\mathrm{ln}\:{x}}{{x}}{dx} \\ $$$$=\left[\frac{{x}^{\mathrm{2}} }{\mathrm{2}}{e}^{{t}} −\frac{\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}} }{\mathrm{2}}\right]_{\mathrm{1}} ^{{e}} =\left[\frac{{e}^{\mathrm{2}} {e}^{{t}} }{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}−\left(\frac{{e}^{{t}} }{\mathrm{2}}−\mathrm{0}\right)\right] \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\left({e}^{{t}+\mathrm{2}} −{e}^{{t}} −\mathrm{1}\right) \\ $$ | ||