Question Number 113203 by abdomsup last updated on 11/Sep/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}} \\ $$ Answered by 1549442205PVT last updated on 11/Sep/20 $$\mathrm{Consider}\:\mathrm{f}\left(\mathrm{z}\right)=\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{4}} +\mathrm{2z}^{\mathrm{2}}…
Question Number 113198 by mnjuly1970 last updated on 11/Sep/20 $$\:\:\:\:\:\:\:\:\:….\:{calculus}…. \\ $$$$\:\:\:\:\:\:\mathscr{E}{valuate}\:::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{I}\::=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt{{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)+\mathrm{1}}−\mathrm{3}{x}}{dx}=??? \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\mathscr{M}.\mathscr{N}.{july}\:\mathrm{1970}# \\ $$$$\:\: \\…
Question Number 47651 by prof Abdo imad last updated on 12/Nov/18 $${calculate}\:\:{A}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{sin}\left(\left[{nx}\right]\right){e}^{−\mathrm{2}{x}} {dx}\:{with}\:{n} \\ $$$${integr}\:{natural}\:. \\ $$ Commented by maxmathsup by imad…
Question Number 178712 by mnjuly1970 last updated on 20/Oct/22 Answered by mr W last updated on 20/Oct/22 $$\frac{\mathrm{1}}{{n}}\left(\frac{\mathrm{1}}{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}\right)=\frac{\mathrm{1}}{\mathrm{2}{n}}\left(\frac{\mathrm{1}}{\mathrm{2}{n}−\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{1}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{2}{n}−\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{1}}−\frac{\mathrm{1}}{{n}} \\ $$$$ \\ $$$$\underset{{n}=\mathrm{1}}…
Question Number 178693 by peter frank last updated on 20/Oct/22 $$\mathrm{P}{rove}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{tan}\:\mathrm{2x}}{\:\sqrt{\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}+\mathrm{4cos}\:^{\mathrm{2}} \mathrm{x}}\:−\sqrt{\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}+\mathrm{4sin}\:^{\mathrm{2}} \mathrm{x}}}=\mathrm{1} \\ $$ Commented by peter frank…
Question Number 178692 by peter frank last updated on 20/Oct/22 $$\int\frac{\mathrm{tan}\:\left(\mathrm{ln}\:{x}\right).\mathrm{tan}\:\left(\mathrm{ln}\:\frac{{x}}{\mathrm{2}}\right).\mathrm{tan}\:\left(\mathrm{ln}\:\mathrm{2}\right)}{{x}}{dx} \\ $$$$ \\ $$ Answered by mindispower last updated on 21/Oct/22 $${tg}\left({ln}\left(\frac{{x}}{\mathrm{2}}\right)+{ln}\left(\mathrm{2}\right)\right)={tg}\left({lnx}\right)=\frac{{tg}\left({ln}\left[\left(\mathrm{2}\right)\right)+{tgg}\left({ln}\left(\frac{{x}}{\mathrm{2}}\right)\right)\right.}{\mathrm{1}−{tg}\left({ln}\left(\mathrm{2}\right)\right){tg}\left({ln}\left(\frac{{x}}{\mathrm{2}}\right)\right)} \\ $$$$\Leftrightarrow{tg}\left({ln}\left({x}\right)\right){tg}\left({ln}\left(\frac{{x}}{\mathrm{2}}\right)\right){tgln}\mathrm{2}=−{tgln}\left(\mathrm{2}\right)−{tgln}\frac{{x}}{\mathrm{2}}…
Question Number 113159 by Dwaipayan Shikari last updated on 11/Sep/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{2}} {log}\left(\mathrm{1}−{x}\right){dx} \\ $$ Answered by MJS_new last updated on 11/Sep/20 $$\int{x}^{\mathrm{2}} \mathrm{ln}\:\left(\mathrm{1}−{x}\right)\:{dx}=…
Question Number 47595 by ajfour last updated on 12/Nov/18 Commented by ajfour last updated on 12/Nov/18 $${Regarding}\:{Q}.\mathrm{47497}\:\left({some}\:{analysis}\right) \\ $$$${Also}\:{see}\:{diagram}\:{of}\:{Q}.\mathrm{47599}\: \\ $$$${for}\:{part}\:{of}\:{solution}\left({section}\:{A}\right). \\ $$ Commented by…
Question Number 178657 by mnjuly1970 last updated on 19/Oct/22 $$ \\ $$$$\:\:\:\:\:\:{calculate} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{I}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{\:\:\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{1}+\:\mathrm{tan}\left(\mathrm{2x}\right)}\:\mathrm{dx}\:=\:? \\ $$$$\: \\ $$ Terms of Service…
Question Number 113110 by gopikrishnan last updated on 11/Sep/20 $$\overset{\mathrm{1}} {\int}_{\mathrm{0}} \sqrt{{x}\left({x}−\mathrm{1}\right){dx}} \\ $$ Commented by 1549442205PVT last updated on 11/Sep/20 $$\mathrm{The}\:\mathrm{function}\:\sqrt{\mathrm{x}\left(\mathrm{x}−\mathrm{1}\right)}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{on} \\ $$$$\mathrm{set}\:\mathrm{X}=\left(−\infty,\mathrm{0}\right]\cup\left[\mathrm{1},+\infty\right)\:\mathrm{and}\:\mathrm{isn}'\mathrm{t} \\…