Question Number 335 by Vishal Bhardwaj last updated on 22/Dec/14 $$\int\:\frac{\sqrt{\left({x}^{\mathrm{2}} +\mathrm{1}\right)}\left[{ln}\left({x}^{\mathrm{2}} +\mathrm{1}\right)−\mathrm{2}{lnx}\right]}{{x}^{\mathrm{4}} }\:{dx} \\ $$ Commented by 123456 last updated on 22/Dec/14 $$\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}{{x}^{\mathrm{4}}…
Question Number 131405 by bramlexs22 last updated on 04/Feb/21 $$ \\ $$$$\:\:\ldots\ldots\:\:\mathrm{super}\:\mathrm{cooles}\:\mathrm{Integral}\:\iddots\iddots \\ $$$$\:\int_{\mathrm{0}} ^{\:\infty} \frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\:=? \\ $$ Commented by bramlexs22 last updated…
Question Number 131401 by mnjuly1970 last updated on 04/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:\:{prove}\:\:{that}::: \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\mathscr{A}{rcsin}\left({x}\right)\right).\left(\mathscr{A}{rccos}\left({x}\right)\right){dx}\overset{??} {=}\mathrm{2}−\frac{\pi}{\mathrm{2}} \\ $$$$ \\ $$ Answered by mathmax by…
Question Number 325 by 123456 last updated on 25/Jan/15 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{x}^{\mathrm{3}} \mathrm{ln}\:{x}\:{dx}+\underset{\mathrm{1}} {\overset{\infty} {\int}}{x}^{\mathrm{3}} {e}^{{x}−\mathrm{1}} {dx} \\ $$ Answered by prakash jain last updated…
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 $$\int{xe}^{{t}} {dx}−\int\frac{\mathrm{ln}\:{x}}{{x}}{dx}…
Question Number 313 by Vishal Bhardwaj last updated on 25/Jan/15 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {log}\:{sin}\theta\:{d}\theta \\ $$ Answered by prakash jain last updated on 20/Dec/14 $${I}=\int_{\mathrm{0}} ^{\pi/\mathrm{2}}…
Question Number 307 by userid1 last updated on 25/Jan/15 $$\mathrm{Evaluate}\:\underset{\mathrm{0}} {\overset{\infty} {\int}}{te}^{−\mathrm{3}{t}} \mathrm{cos}\:{t}\:{dt} \\ $$ Commented by 123456 last updated on 20/Dec/14 $$\underset{\mathrm{0}} {\overset{\infty} {\int}}{te}^{−\mathrm{3}{t}}…
Question Number 65834 by ~ À ® @ 237 ~ last updated on 04/Aug/19 $$\:\:\:\forall\:\:{x},\:{y}\:\:>\mathrm{0}\:\:\:\:{B}\left({x},{y}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:{t}^{{x}−\mathrm{1}} \left(\mathrm{1}−{t}\right)^{{y}−\mathrm{1}} {dt}\:\:\:\:\:\:\Gamma\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:{t}^{{x}−\mathrm{1}} \:{e}^{−{t}} {dt} \\ $$$$\left.\mathrm{1}\right)\:{show}\:{that}\:\:\forall\:{x}>\mathrm{0}\:\:\:\:\Gamma\left({x}+\mathrm{1}\right)={x}\Gamma\left({x}\right)\:\:\:\:{and}\:\:{lim}_{{n}−>\infty}…
Question Number 65837 by mathmax by abdo last updated on 04/Aug/19 $$\left.\mathrm{1}\right)\:{calculate}\:\int_{−\infty} ^{\infty} \:\frac{{dx}}{\mathrm{1}+{ix}}\:\:{and}\:\int_{−\infty} ^{\infty} \:\:\frac{{dx}}{\mathrm{1}−{ix}} \\ $$$$\left.\mathrm{2}\right){deduce}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{\infty} \:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right){calculate}\:\int_{−\infty} ^{\infty} \:\:\frac{{dx}}{\mathrm{1}+{ix}^{\mathrm{2}}…
Question Number 65828 by ~ À ® @ 237 ~ last updated on 04/Aug/19 $$\:{Let}\:{go}\:{toward}\:{a}\:{rational}\:{order}\:{of}\:{derivation} \\ $$$$ \\ $$$${Part}\:\mathrm{1}\::\:\:{What}'{s}\:{that}\:{special}\:{factor}\:\: \\ $$$${Let}\:{n}\:,\:{p}\:{and}\:{k}\:{three}\:{integer}\:\:{different}\:{of}\:{zero} \\ $$$${We}\:\:{state}\:{J}_{{n},{k}} \left({p}\right)=\int_{\mathrm{0}} ^{\mathrm{1}}…