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Question Number 36428 Answers: 2 Comments: 1
$${find}\:\:\int\:\:\:\:\frac{{dx}}{{cos}^{\mathrm{4}} {x}\:+{sin}^{\mathrm{4}} {x}} \\ $$
Question Number 36427 Answers: 1 Comments: 1
$${calculate}\:\int_{\frac{\pi}{\mathrm{8}}} ^{\frac{\pi}{\mathrm{6}}} \:\:\:\frac{{dx}}{{sin}\left(\mathrm{2}{x}\right)} \\ $$
Question Number 36426 Answers: 1 Comments: 0
$${find}\:\:\int\:{x}^{\mathrm{2}} \sqrt{\mathrm{1}+{x}^{\mathrm{3}} \:}\:{dx} \\ $$
Question Number 36425 Answers: 2 Comments: 2
$${calculate}\:\int_{\mathrm{1}} ^{\mathrm{4}} \:\:\:\frac{{x}\sqrt{{x}}}{{x}^{\mathrm{2}} \:−\mathrm{5}{x}\:+\mathrm{4}}{dx} \\ $$
Question Number 36424 Answers: 0 Comments: 2
$${find}\:\int\:\:{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{2}} −\mathrm{1}}{dx} \\ $$
Question Number 36423 Answers: 0 Comments: 0
$${find}\:\int\:\:\:\:\:\frac{{dt}}{{t}\sqrt{{t}^{\mathrm{2}} \:+{t}+\mathrm{1}}} \\ $$
Question Number 36422 Answers: 0 Comments: 1
$${find}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{{x}} \left({t}^{\mathrm{2}} +\mathrm{1}\right){arctan}\left({t}\right){dt}\:. \\ $$
Question Number 36421 Answers: 0 Comments: 1
$${find}\:\int\:\:\:\:\frac{{dx}}{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{1}−{x}}} \\ $$
Question Number 36420 Answers: 0 Comments: 0
$${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \frac{\:{arctan}\left({xt}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{4}} }{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right). \\ $$
Question Number 36419 Answers: 0 Comments: 3
$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\left(\mathrm{2}{x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{3}} }{dx} \\ $$
Question Number 36418 Answers: 1 Comments: 0
$${calculate}\:\:\int_{−\mathrm{3}} ^{\mathrm{4}} \mid{x}^{\mathrm{2}} \:−\mathrm{2}{x}−\mathrm{3}\mid{dx} \\ $$
Question Number 36417 Answers: 1 Comments: 1
$${calculate}\:\int_{\mathrm{2}} ^{\mathrm{6}} \:\:\:\frac{{dx}}{\sqrt{{x}+\mathrm{1}}\:+\sqrt{{x}−\mathrm{1}}} \\ $$
Question Number 36416 Answers: 0 Comments: 0
$${calculate}\:{I}\:=\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\:\frac{\mathrm{2}{x}^{\mathrm{3}} \:+\mathrm{5}{x}^{\mathrm{2}} \:−\mathrm{4}{x}−\mathrm{7}}{\left({x}+\mathrm{2}\right)^{\mathrm{2}} }{dx} \\ $$
Question Number 36415 Answers: 0 Comments: 1
$${calculate}\:{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left({x}^{\mathrm{3}} \:+{x}\right){cos}^{\mathrm{2}} {xdx}\:{and} \\ $$$${J}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\left({x}^{\mathrm{3}} \:+{x}\right){sin}^{\mathrm{2}} {xdx} \\ $$$${cslculate}\:{I}\:{and}\:{J}\:. \\ $$
Question Number 36413 Answers: 0 Comments: 1
$${let}\:\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{n}} \sqrt{\mathrm{3}+{x}}{dx} \\ $$$$\left.\mathrm{1}\right){calculate}\:{lim}_{{n}\rightarrow+\infty} {I}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:{n}\:{I}_{{n}} \\ $$
Question Number 36412 Answers: 1 Comments: 1
$${calculate}\:{I}_{\lambda} \:=\int_{\mathrm{0}} ^{\lambda} \:{e}^{−{x}} {ln}\left(\mathrm{1}+{e}^{{x}} \right){dx} \\ $$
Question Number 36411 Answers: 0 Comments: 0
$${calculate}\:\int_{\mathrm{1}} ^{\mathrm{3}} \:\:\:\frac{{x}−\mathrm{1}}{\mid{x}^{\mathrm{2}} −\mathrm{2}{x}\mid\:+\mathrm{1}}{dx} \\ $$
Question Number 36410 Answers: 0 Comments: 1
$${find}\:{the}\:{value}\:{of}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{n}} \sqrt{\mathrm{1}−{x}}{dx} \\ $$
Question Number 36406 Answers: 2 Comments: 1
$${find}\:{the}\:{values}\:{of}\:\:{I}\:=\:\int_{\mathrm{0}} ^{\pi} {cos}^{\mathrm{4}} {dx}\:{and} \\ $$$${J}\:=\:\int_{\mathrm{0}} ^{\pi} \:{sin}^{\mathrm{4}} {dx}\:. \\ $$
Question Number 36398 Answers: 1 Comments: 1
$${Consider}\:{triangle}\:{ABC}.{If}\:\mathrm{206} \\ $$$${lines}\:{are}\:{drawn}\:{from}\:{A}\:{to}\:{BC}\:{how} \\ $$$${many}\:{triangles}\:{are}\:{formed}? \\ $$
Question Number 36397 Answers: 2 Comments: 0
$${find}\:{I}\:\:=\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\:\:\:\:\frac{{dx}}{{x}\sqrt{{x}+\mathrm{1}}\:\:+\left({x}+\mathrm{1}\right)\sqrt{{x}}} \\ $$$$ \\ $$
Question Number 36394 Answers: 0 Comments: 0
$${let}\:{f}\left({x}\right)={artanx}\:{find}\:\:{L}\left({f}\left({x}\right)\right) \\ $$$${L}\:{mean}\:{laplace}\:{trsnsform}. \\ $$
Question Number 36393 Answers: 0 Comments: 0
$${let}\:{f}\left({x}\right)\:=\:\frac{\mathrm{2}}{{sinx}}\:\:\:,\mathrm{2}\pi\:{periodic}\:{odd} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie}\:. \\ $$
Question Number 36389 Answers: 0 Comments: 0
$$\:\mathrm{If}\:\mu\:\mathrm{is}\:\mathrm{a}\:\mathrm{universal}\:\mathrm{set}\:\mathrm{and}\:\mathrm{A},\mathrm{B},\mathrm{C}\:\mathrm{are} \\ $$$$\mathrm{3}\:\mathrm{sets}\:.\:\:\:\mathrm{Given}\:\mathrm{that}\: \\ $$$$\mathrm{n}\left(\mu\right)=\:\mathrm{52}\:\:,\:\mathrm{n}\left(\mathrm{A}\cap\mathrm{B}\right)\:=\:\mathrm{26}\:\mathrm{and}\: \\ $$$$\mathrm{n}\left(\mathrm{A}\:\cup\:\mathrm{C}\right)\:=\:\mathrm{32}\:\mathrm{find}\:\mathrm{n}\left(\mathrm{A}\right),\mathrm{n}\left(\mathrm{B}\right)\:\mathrm{and} \\ $$$$\mathrm{n}\left(\mathrm{C}\right) \\ $$
Question Number 36385 Answers: 1 Comments: 1
Question Number 36387 Answers: 0 Comments: 0
$$\mathbb{DANILA} \\ $$
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