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Category: Integration

Question-88388

Question Number 88388 by M±th+et£s last updated on 10/Apr/20 Answered by mind is power last updated on 10/Apr/20 $$\mathrm{49}{sec}^{\mathrm{2}} \left({x}\right)+\mathrm{28}{tan}\left({x}\right)+\mathrm{9}{sin}^{\mathrm{2}} \left({x}\right)−\mathrm{6}{sin}\left({x}\right)−\mathrm{44} \\ $$$$=\mathrm{49}\left(\mathrm{1}+{tg}^{\mathrm{2}} \left({x}\right)\right)+\mathrm{28}{tg}\left({x}\right)+\left(\mathrm{3}{sin}\left({x}\right)−\mathrm{1}\right)^{\mathrm{2}} −\mathrm{45}…

0-a-p-1-p-2-x-2n-p-2-dx-1-lt-2n-lt-n-1-

Question Number 153893 by Tawa11 last updated on 11/Sep/21 $$\int_{\:\mathrm{0}} ^{\:\:\infty} \mathrm{a}\:\underset{\mathrm{p}\:\rightarrow\:\mathrm{1}} {\overset{\infty} {\prod}}\left(\frac{\mathrm{p}^{\mathrm{2}} \:\:−\:\:\:\mathrm{x}^{\mathrm{2n}} }{\mathrm{p}^{\mathrm{2}} }\right)\mathrm{dx},\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}\:\:<\:\:\mathrm{2n}\:\:<\:\:\mathrm{n}\:\:+\:\:\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact:…

1-4-dx-4x-1-x-

Question Number 88357 by jagoll last updated on 10/Apr/20 $$\int\underset{\mathrm{1}} {\overset{\mathrm{4}} {\:}}\:\frac{\mathrm{dx}}{\left(\mathrm{4x}−\mathrm{1}\right)\sqrt{\mathrm{x}}} \\ $$ Commented by john santu last updated on 10/Apr/20 $$\left[\:{t}=\sqrt{{x}}\:,\:\mathrm{2}{t}\:{dt}\:=\:{dx}\:\right]\: \\ $$$$\underset{\mathrm{1}}…

Prove-that-1-ln-x-x-pi-1-ln-2-x-1-2-dx-pi-2-8-16-

Question Number 153875 by mnjuly1970 last updated on 11/Sep/21 $$ \\ $$$$\:\:\:\:\mathrm{Prove}\:\:\mathrm{that}.. \\ $$$$\:\:\: \\ $$$$\:\:\:\:\boldsymbol{\phi}\::\:=\int_{\:\mathrm{1}} ^{\:+\infty} \frac{\:{ln}\:\left({x}\:\right)}{\left(\:{x}^{\:\pi} \:−\mathrm{1}\:\right)\left(\:{ln}^{\:\mathrm{2}} \left({x}\right)\:+\mathrm{1}\:\right)^{\mathrm{2}} }{dx}=\:\frac{\pi^{\:\mathrm{2}} −\:\mathrm{8}}{\mathrm{16}}\:\:\:\:\:\:\:\:\:\blacksquare\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\: \\…

x-2-x-2-5-2-x-3-2-dx-

Question Number 88307 by M±th+et£s last updated on 09/Apr/20 $$\int\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} −\frac{\mathrm{5}}{\mathrm{2}}{x}−\frac{\mathrm{3}}{\mathrm{2}}}\:{dx} \\ $$ Answered by TANMAY PANACEA. last updated on 09/Apr/20 $$\int\frac{\mathrm{2}{x}^{\mathrm{2}} }{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{5}{x}−\mathrm{3}}…

Question-88286

Question Number 88286 by Chi Mes Try last updated on 09/Apr/20 Commented by abdomathmax last updated on 09/Apr/20 $${U}_{{n}} =\left\{\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}+\mathrm{1}} −\mathrm{1}−\frac{\mathrm{1}}{{n}}\right\}^{−{n}} \\ $$$$\Rightarrow{U}_{{n}} ={e}^{−{nln}\left\{\:\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}+\mathrm{1}} −\mathrm{1}−\frac{\mathrm{1}}{{n}}\right\}\:\:}…