Question Number 189496 by Tawa11 last updated on 17/Mar/23 $$\int\:\mathrm{xe}^{\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}} \:\mathrm{dx} \\ $$ Answered by BaliramKumar last updated on 18/Mar/23 $${let}\:\:\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\:=\:{y} \\ $$$$\frac{\mathrm{2}{x}}{\mathrm{2}}\:=\:\frac{{dy}}{{dx}}\:\Rightarrow\:{xdx}\:=\:{dy}…
Question Number 189489 by mnjuly1970 last updated on 17/Mar/23 $$ \\ $$$$\:\:\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\infty} {e}^{\:−{x}} {cos}\left({x}\right){ln}\left({x}\right){dx}=? \\ $$$$\:\:\:\:\:−−− \\ $$$$\:\:\:\:\:\:{f}\:\left({a}\:\right)=\:\int_{\mathrm{0}} ^{\:\infty} {e}^{\:−{x}} {cos}\left({x}\right){x}^{\:{a}} \:{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…
Question Number 123937 by mnjuly1970 last updated on 29/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:\:\:\:\:{calculus}… \\ $$$$\:{prove}\:{that}:: \\ $$$$\:\int_{\frac{−\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \frac{\left(\pi−\mathrm{4}{x}\right){tan}\left({x}\right)}{\mathrm{1}−{tan}\left({x}\right)}{dx}\overset{???} {=}\pi{ln}\left(\mathrm{2}\right)−\frac{\pi^{\mathrm{2}} }{\mathrm{4}} \\ $$$$ \\ $$ Answered by Dwaipayan…
Question Number 123921 by john_santu last updated on 29/Nov/20 $$\int\:\frac{\mathrm{1}}{\:\sqrt{{x}}\:\left({x}+\mathrm{1}\right)\left(\left(\mathrm{tan}^{−\mathrm{1}} \sqrt{{x}}\right)^{\mathrm{2}} +\mathrm{9}\right)}{dx} \\ $$ Answered by mindispower last updated on 29/Nov/20 $$=\int\frac{\mathrm{2}}{\left({t}^{\mathrm{2}} +\mathrm{1}\right)\left({tan}^{−} \left({t}\right)^{\mathrm{2}} +\mathrm{9}\right)}\:…
Question Number 123920 by john_santu last updated on 29/Nov/20 $$\:\int\:\frac{\left({x}−\mathrm{1}\right)\sqrt{{x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}}}{{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)}\:{dx}\:? \\ $$ Answered by liberty last updated on 29/Nov/20 $$\left(\bullet\right)\:\frac{{x}−\mathrm{1}}{{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)}\:=\:\frac{{x}^{\mathrm{2}}…
Question Number 123900 by mnjuly1970 last updated on 29/Nov/20 $$\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:{integral}… \\ $$$$\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}^{\mathrm{2}} \left({x}\right)}{{x}^{\mathrm{2}} \left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{dx}\:=\frac{\pi}{\mathrm{4}}\left(\mathrm{1}+\frac{\pi}{{e}^{\mathrm{2}} }\right) \\ $$ Answered by mathmax…
Question Number 123896 by john_santu last updated on 29/Nov/20 $$\:\:\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{\mathrm{sin}\:^{\mathrm{2}} {x}}{\:\sqrt{{x}}}\:{dx} \\ $$ Answered by mindispower last updated on 29/Nov/20 $${sin}^{\mathrm{2}} \left({x}\right)=\frac{\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}} \\…
Question Number 189418 by TUN last updated on 16/Mar/23 $${Know}:\:{f}\left({x}\right)=\mathrm{3}{x}+\mathrm{2}+\underset{\mathrm{0}} {\int}^{\mathrm{1}} {xf}\left({x}\right){dx} \\ $$$${Eluavte}:\:\underset{\mathrm{0}} {\int}^{\mathrm{2}} {f}\left({x}\right){dx}=¿ \\ $$ Answered by mr W last updated on…
Question Number 123866 by benjo_mathlover last updated on 28/Nov/20 $$\:{To}\:{mr}\:{mjs}\:{sir}.\: \\ $$$${integral}\:{lover}\: \\ $$$$\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\frac{\mathrm{tan}\:\left(\frac{\pi}{\mathrm{4}}−{x}\right)}{\mathrm{cos}\:^{\mathrm{2}} {x}\:\sqrt{\mathrm{tan}\:^{\mathrm{3}} {x}+\mathrm{tan}\:^{\mathrm{2}} {x}+\mathrm{tan}\:{x}}}\:{dx}\:=?\: \\ $$ Answered by liberty last…
Question Number 123859 by sdfg last updated on 28/Nov/20 $$\int{sect}\:{e}^{{t}} \:{dt} \\ $$ Answered by mindispower last updated on 29/Nov/20 $${sec}\left({x}\right)=\frac{\mathrm{2}}{{e}^{{ix}} +{e}^{−{ix}} },{we}\:{use}\:{cos}\left({x}\right)=\frac{{e}^{{ix}} +{e}^{−{ix}} }{\mathrm{2}}…