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Category: Integration

x-1-x-3-dx-

Question Number 152660 by Tawa11 last updated on 30/Aug/21 $$\int\:\frac{\mathrm{x}}{\:\sqrt{\mathrm{1}\:\:\:+\:\:\:\mathrm{x}^{\mathrm{3}} }}\:\mathrm{dx} \\ $$ Answered by Olaf_Thorendsen last updated on 31/Aug/21 $$\left(\mathrm{1}+{u}\right)^{−\frac{\mathrm{1}}{\mathrm{2}}} \:=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \frac{\left(\mathrm{2}{n}\right)!}{\mathrm{2}^{\mathrm{2}{n}}…

pi-2-pi-4-3x-7-

Question Number 21582 by Isse last updated on 28/Sep/17 $$\int_{\pi/\mathrm{2}} ^{\pi/\mathrm{4}} \left(\mathrm{3}{x}+\mathrm{7}\right) \\ $$ Answered by Joel577 last updated on 29/Sep/17 $${I}\:=\:\underset{\frac{\pi}{\mathrm{2}}} {\overset{\frac{\pi}{\mathrm{4}}} {\int}}\:\mathrm{3}{x}\:+\:\mathrm{7}\:{dx} \\…

dx-1-x-x-x-2-

Question Number 87103 by hamdhan last updated on 02/Apr/20 $$\int\frac{{dx}}{\left(\mathrm{1}+{x}\right)\sqrt{{x}−{x}^{\mathrm{2}} }} \\ $$ Commented by abdomathmax last updated on 02/Apr/20 $${I}\:=\int\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{−\left({x}^{\mathrm{2}} −{x}\right)}}\:=\int\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{−\left({x}^{\mathrm{2}} −{x}\:+\frac{\mathrm{1}}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{4}}\right)}} \\ $$$$=\int\:\:\:\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{\frac{\mathrm{1}}{\mathrm{4}}−\left({x}−\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}}…

Question-87086

Question Number 87086 by Chi Mes Try last updated on 02/Apr/20 Answered by mind is power last updated on 03/Apr/20 $$=\int_{\mathrm{0}} ^{+\infty} \mathrm{2}\frac{{dt}}{\left({t}^{\mathrm{4}} +\left(\mathrm{1}+\mathrm{2}\sqrt{\mathrm{2}}\right){t}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{1}−{t}^{\mathrm{2}}…