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IntegrationQuestion and Answers: Page 202
Question Number 79929 Answers: 0 Comments: 0
$$\int{e}^{\sqrt{\mathrm{sin}\:{x}}} {dx}=? \\ $$
Question Number 79913 Answers: 0 Comments: 1
$$\:{Convergence}\:\:{of}\:\:{I}=\int_{\mathrm{0}} ^{\:\infty} \frac{{e}^{{t}} }{{e}^{−{t}} +{e}^{\mathrm{2}{t}} \mid{sint}\mid}{dt} \\ $$
Question Number 79903 Answers: 1 Comments: 11
Question Number 79869 Answers: 0 Comments: 1
$${For}\:\:{witch}\:\:{value}\:\:{of}\:\:\alpha\:\:{the}\:\:{integral} \\ $$$$\:\:{I}=\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{1}}{\sqrt{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }}−\frac{\alpha}{\mathrm{1}+{x}}\right){dx}\:\:{converge}; \\ $$$$\:\:{and}\:\:{in}\:\:{this}\:\:{case}\:\:{calculate}\:\:\alpha \\ $$
Question Number 79837 Answers: 1 Comments: 10
Question Number 79825 Answers: 0 Comments: 4
$$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\sqrt{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{1}}\:\:\mathrm{dx} \\ $$
Question Number 79824 Answers: 2 Comments: 7
Question Number 79814 Answers: 0 Comments: 5
Question Number 79763 Answers: 1 Comments: 2
$${calculate}\:\int_{\mathrm{0}} ^{\pi} \left\{{cos}^{\mathrm{8}} {x}\:+{sin}^{\mathrm{8}} {x}\right\}{dx} \\ $$
Question Number 79758 Answers: 0 Comments: 1
$${find}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{ix}^{\mathrm{2}} \right){dx}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{ix}^{\mathrm{2}} \right){dx}\:{with}\:{i}=\sqrt{−\mathrm{1}} \\ $$
Question Number 79730 Answers: 1 Comments: 1
$$\left.{I}\right)\:\:{For}\:{witch}\:{value}\:{of}\:\alpha\:{the}\:{integral} \\ $$$$\:{C}=\int_{\mathrm{0}} ^{\:\infty} \left(\frac{\mathrm{1}}{\sqrt{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }}−\frac{\mathrm{1}}{{x}+\mathrm{1}}\right){dx}\:\:{conveege}\:\:? \\ $$$${And}\:{in}\:{this}\:{case}\:{calculate}\:\alpha. \\ $$$$\left.{II}\right)\:\:{Let}\:\Delta=\left\{\left({x};\:{y}\right)/\:\mid{x}\mid+\mid{y}\mid\leqslant\mathrm{2}\right\} \\ $$$$\left.\:\:\:\:\:{a}\right)\:{Calculate}\:{I}_{\mathrm{1}} =\:\int\int_{\Delta} {dxdy}\:\:\:{and}\:\:\int\int_{\Delta} \frac{{dxdy}}{\left(\mid{x}\mid+\mid{y}\mid\right)^{\mathrm{2}} +\mathrm{4}} \\ $$
Question Number 79646 Answers: 0 Comments: 1
$${calculate}\:\:{A}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:{cos}\left({narcosx}\right){dx} \\ $$$${with}\:{n}\:{integr}\:{natural} \\ $$
Question Number 79645 Answers: 0 Comments: 0
$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{ln}\left(\mathrm{1}+{x}^{\mathrm{4}} \right){dx} \\ $$
Question Number 79634 Answers: 1 Comments: 3
Question Number 79627 Answers: 0 Comments: 2
$$\left.\mathrm{1}\right)\:{expicite}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:{with}\:{x}\geqslant\mathrm{0} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+\mathrm{2}{t}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$
Question Number 79615 Answers: 0 Comments: 3
$${prove}\:{that}\:{with}\:{using}\:{hypergeometric}\:{function} \\ $$$$\int_{\mathrm{0}} ^{\pi} {sin}\left({x}^{\mathrm{2}} \right)=\frac{\pi^{\mathrm{3}} }{\mathrm{3}}\:\mathrm{1}{F}_{\mathrm{2}} \left[\frac{\mathrm{3}}{\mathrm{4}};\frac{\mathrm{3}}{\mathrm{2}};\frac{\mathrm{7}}{\mathrm{4}};\frac{−\pi^{\mathrm{4}} }{\mathrm{4}}\right]\: \\ $$
Question Number 79607 Answers: 0 Comments: 1
$${Solve}\:{this} \\ $$$$\int_{} \frac{\left({x}−{yz}\right)}{\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{xyz}\right)^{\mathrm{3}/\mathrm{2}} }{dz} \\ $$$$ \\ $$$$ \\ $$
Question Number 79580 Answers: 0 Comments: 5
$$\mathrm{does}\:\mathrm{this}\:\mathrm{matter}\:\mathrm{reasonable} \\ $$$$\int\:\mathrm{sin}\:^{\mathrm{x}} \left(\mathrm{x}\right)\:\mathrm{dx}\:? \\ $$
Question Number 79612 Answers: 1 Comments: 0
$$\int\:\frac{\mathrm{dx}}{\sqrt{\mathrm{x}\:}\left(\sqrt[{\mathrm{4}\:}]{\mathrm{x}}+\mathrm{1}\right)^{\mathrm{10}} }\:=\:? \\ $$
Question Number 79531 Answers: 0 Comments: 1
$$\underset{\mathrm{0}} {\int}^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\frac{\mathrm{1}}{\mathrm{x}}+\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{dx}\:? \\ $$
Question Number 79528 Answers: 0 Comments: 0
$${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{x}^{\mathrm{3}} } {cos}\left({x}^{\mathrm{2}} \right){dx} \\ $$
Question Number 79527 Answers: 0 Comments: 1
$${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{x}^{\mathrm{3}} } {dx} \\ $$
Question Number 79520 Answers: 1 Comments: 2
Question Number 79516 Answers: 0 Comments: 3
Question Number 79500 Answers: 1 Comments: 0
$$\int\left(\mathrm{cot}\:^{\mathrm{2}} {x}+\mathrm{cot}\:^{\mathrm{4}} {x}\right){dx} \\ $$
Question Number 79485 Answers: 1 Comments: 0
$$\int\left(\mathrm{tan}\:^{\mathrm{2}} {x}+\mathrm{tan}\:^{\mathrm{4}} {x}\right){dx} \\ $$
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