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Question Number 46856 Answers: 0 Comments: 1
$${find}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{\mathrm{2}} \:{arctan}\left(\mathrm{1}+{tx}\right){dx}\: \\ $$
Question Number 46855 Answers: 0 Comments: 1
$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}\:{arctan}\left(\mathrm{1}+{x}\right){dx} \\ $$
Question Number 46854 Answers: 1 Comments: 1
$${find}\:\:=\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{sinx}}{\mathrm{2}+{cos}\left(\mathrm{2}{x}\right)}{dx} \\ $$
Question Number 46853 Answers: 1 Comments: 1
$${fnd}\:\:\int\:\:\:\:\:\:\frac{{dx}}{\mathrm{1}+{cos}\left({tx}\right)} \\ $$
Question Number 46852 Answers: 1 Comments: 1
$${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{n}^{\mathrm{3}} }{\mathrm{3}^{{n}} } \\ $$
Question Number 46851 Answers: 0 Comments: 3
$${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sint}}{{x}\:+{sint}}{dt}\:\:{withx}>\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{sint}}{\left({x}+{sint}\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sint}}{\mathrm{2}+{sint}}{dt}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sint}}{\left(\mathrm{2}+{sint}\right)^{\mathrm{2}} }{dt} \\ $$
Question Number 46850 Answers: 1 Comments: 1
$${let}\:{a}^{\mathrm{2}} >{b}^{\mathrm{2}\:} +{c}^{\mathrm{2}} \:\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{d}\theta}{{a}+{bsin}\theta\:+{c}\:{cos}\theta} \\ $$
Question Number 46849 Answers: 0 Comments: 0
$$\left.{let}\:{A}_{{p}} =\sum_{{n}=\mathrm{1}} ^{\infty} \:{n}^{{p}} {x}^{{n}} \:\:\:\:{with}\:{p}\:{integr}\:.\:{and}\:{x}\:\in\right]−\mathrm{1},\mathrm{1}\left[\:.\right. \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{\mathrm{1}} ,{A}_{\mathrm{2}} \:{and}\:{A}_{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{relation}\:{of}\:{recurrence}\:\:{betwen}\:{the}\:{A}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{n}^{\mathrm{4}} {x}^{{n}} \:{and}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{n}^{\mathrm{5}} {x}^{{n}} \:. \\ $$
Question Number 46848 Answers: 0 Comments: 1
$${caculate}\:\:\int\int_{{D}} \:\:\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)\:{e}^{−{x}^{\mathrm{2}} \:−{y}^{\mathrm{2}} } {dxdy}\:\:{with} \\ $$$${D}\:=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\:\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant\mathrm{4}\right\} \\ $$
Question Number 46847 Answers: 0 Comments: 1
$${calculate}\:\:\int\int_{\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:{and}\:\mathrm{1}\leqslant{y}\leqslant\mathrm{2}} \:\:{e}^{\frac{{x}}{{y}}} {dxdy} \\ $$
Question Number 46846 Answers: 0 Comments: 1
$${calculate}\:\int\int_{{D}} \:\:\:\:\frac{{x}+{y}}{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }}{dxdy}\:{with}\:{D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /{x}\geqslant\mathrm{0},{y}\geqslant\mathrm{0},{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} <\mathrm{1}\right\} \\ $$
Question Number 46845 Answers: 0 Comments: 0
$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{e}^{−{x}} }{\mathrm{1}+{x}}\:{dx}\:. \\ $$
Question Number 46844 Answers: 0 Comments: 1
$${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\mathrm{2}{t}} {ln}\left(\mathrm{1}+\mathrm{3}{t}\right){dt}\: \\ $$
Question Number 46843 Answers: 0 Comments: 0
$${let}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{{x}} \:\frac{{t}}{{sin}\left({t}\right)}{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{t}}{{sint}}{dt} \\ $$
Question Number 46842 Answers: 1 Comments: 1
$${find}\:\:\int\:\:\:\:\:\frac{{dx}}{{x}\sqrt{{x}−{x}^{\mathrm{2}} }} \\ $$
Question Number 46841 Answers: 1 Comments: 1
$${calculate}\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\:\:\frac{{dx}}{{cosx}\:{sinx}} \\ $$
Question Number 46840 Answers: 0 Comments: 1
$${find}\:{lim}_{{n}\rightarrow+\infty} \:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{{n}^{\mathrm{2}\:} +{k}^{\mathrm{2}} }{{n}^{\mathrm{3}} \:+{k}^{\mathrm{3}} } \\ $$
Question Number 46838 Answers: 1 Comments: 0
Question Number 46837 Answers: 0 Comments: 1
$${find}\int\sqrt{{sin}\mathrm{2}{x}}\:{dx}=?? \\ $$
Question Number 46833 Answers: 0 Comments: 1
Question Number 46831 Answers: 0 Comments: 0
Question Number 46829 Answers: 1 Comments: 0
Question Number 46827 Answers: 0 Comments: 0
Question Number 46821 Answers: 1 Comments: 0
Question Number 46816 Answers: 1 Comments: 0
Question Number 46814 Answers: 1 Comments: 0
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