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Category: Integration

let-f-t-0-e-arctsn-1-tx-2-dx-with-t-from-R-1-calculate-f-t-2-find-a-simple-form-of-f-t-

Question Number 35982 by abdo mathsup 649 cc last updated on 26/May/18 $${let}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:{e}^{−{arctsn}\left(\:\mathrm{1}+{tx}^{\mathrm{2}} \right)} {dx}\:\:{with}\:{t}\:{from}\:{R} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{'} \left({t}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({t}\right)\:. \\ $$ Terms…

0-pi-2-1-1-sin-6-x-dx-

Question Number 167040 by cortano1 last updated on 05/Mar/22 $$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}}{\mathrm{1}+\mathrm{sin}\:^{\mathrm{6}} \mathrm{x}}\:\mathrm{dx}=? \\ $$ Commented by greogoury55 last updated on 05/Mar/22 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sec}\:^{\mathrm{6}}…

x-x-x-x-x-x-1-7-1-6-1-5-1-4-1-3-dx-

Question Number 101493 by bemath last updated on 03/Jul/20 $$\int\sqrt{\mathrm{x}.\sqrt[{\mathrm{3}}]{\mathrm{x}.\sqrt[{\mathrm{4}}]{\mathrm{x}.\sqrt[{\mathrm{5}}]{\mathrm{x}.\sqrt[{\mathrm{6}}]{\mathrm{x}.\sqrt[{\mathrm{7}}]{\mathrm{x}…}}}}}}\:\mathrm{dx}\:=\: \\ $$$$ \\ $$ Answered by floor(10²Eta[1]) last updated on 03/Jul/20 $${let}'{s}\:{see}\:{a}\:{small}\:{case}\:{first}\:{to}\:{understand} \\ $$$${better}\:{whats}\:{going}\:{on} \\…

sec-tan-4-d-

Question Number 167024 by peter frank last updated on 04/Mar/22 $$\int\mathrm{sec}\:\theta\mathrm{tan}\:^{\mathrm{4}} \theta\mathrm{d}\theta \\ $$ Answered by cortano1 last updated on 05/Mar/22 $$\:\mathrm{let}\:\mathrm{t}\:=\:\mathrm{tan}\:\theta \\ $$$$\mathrm{I}=\int\:\frac{\mathrm{t}^{\mathrm{4}} }{\:\sqrt{\mathrm{1}+\mathrm{t}^{\mathrm{2}}…