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IntegrationQuestion and Answers: Page 166
Question Number 91771 Answers: 0 Comments: 1
$$\int_{\mathrm{0}} ^{\infty} \frac{{sin}^{\mathrm{3}} \left({x}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$
Question Number 91753 Answers: 1 Comments: 3
$$\int\mathrm{3}\:\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}} \:{dx}\:=\:?? \\ $$
Question Number 91735 Answers: 0 Comments: 1
$$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \sqrt[{{k}}]{\mathrm{tan}^{{m}} \:\alpha}\:{d}\alpha\:{for}\:{m}>\mathrm{1} \\ $$
Question Number 91714 Answers: 0 Comments: 1
Question Number 91703 Answers: 0 Comments: 0
$$\int_{−\infty} ^{+\infty} {f}^{\mathrm{2}} \left({x}\right){dx}\:\forall{f} \\ $$
Question Number 91668 Answers: 0 Comments: 0
$$\int{e}^{{x}^{\mathrm{2}} } \:{erf}\left({x}\right)\:{dx} \\ $$
Question Number 91641 Answers: 0 Comments: 0
$${find}\:\int\:\frac{{cos}^{\mathrm{4}} {x}+{sin}^{\mathrm{4}} {x}}{{cos}^{\mathrm{3}} {x}+{sin}^{\mathrm{3}} {x}}{dx} \\ $$
Question Number 91636 Answers: 0 Comments: 0
$$\int\frac{{dx}}{{x}\left(\sqrt{{x}}+^{\mathrm{5}} \sqrt{{x}^{\mathrm{2}} }\right)} \\ $$
Question Number 91630 Answers: 0 Comments: 1
$$\mathrm{show}\:\mathrm{that}\: \\ $$$$\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{sin2x}}{\left(\mathrm{2}+\mathrm{cos2x}\right)^{\mathrm{2}} }\mathrm{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{x}} \right)\mathrm{dx} \\ $$$$=\frac{\pi}{\mathrm{16}}−\frac{\pi\sqrt{\mathrm{3}}}{\mathrm{36}} \\ $$
Question Number 91621 Answers: 0 Comments: 1
$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:{sin}\left({x}^{\mathrm{6}} \right){dx} \\ $$
Question Number 91620 Answers: 0 Comments: 1
$${let}\:{f}\left({x}\right)\:=\mathrm{2}\:{x}−\sqrt{{x}−\mathrm{1}} \\ $$$${find}\:\int\:\:\frac{{f}\left({x}\right)}{{f}^{−\mathrm{1}} \left({x}\right)}{dx}\:\:{and}\:\:\int\:{ln}\left(\frac{{f}\left({x}\right)}{{f}^{−\mathrm{1}} \left({x}\right)}\right){dx} \\ $$
Question Number 91619 Answers: 0 Comments: 1
$${calculate}\:\int_{\mathrm{2}} ^{+\infty} \:\frac{\left(−\mathrm{1}\right)^{\left[\mathrm{2}{x}\right]} }{{x}\left[{x}\right]−\mathrm{1}}{dx} \\ $$
Question Number 91615 Answers: 0 Comments: 2
$${hi}\:{every}\:{one}\:{is}\:{it}\:{right}\:{if}\:{we}\:{use}\:{tylor} \\ $$$${in}\:{this}\:{integration}\:{and}\:{if}\:{there}\:{were} \\ $$$${another}\:{way}\:{that}\:{will}\:{be}\:{very}\:{cool} \\ $$$$\int{sin}\left({x}^{\mathrm{4}} \right){dx}\: \\ $$$$ \\ $$$$ \\ $$
Question Number 91611 Answers: 0 Comments: 1
$$\:{find}\:{the}\:{volume}\:{of}\:{the}\:{region}\: \\ $$$${between}\:{curves}\:\left({xy}=\mathrm{4}\:{and}\:{x}+{y}=\mathrm{5}\right) \\ $$$${revolvex}\:{around}\:{the}\:{X}\:{axis} \\ $$
Question Number 91603 Answers: 0 Comments: 1
$${calculate}\:\int_{\mathrm{0}} ^{\infty} {xe}^{−{x}^{\mathrm{2}} −\left[{x}\right]} \:{dx} \\ $$
Question Number 91593 Answers: 1 Comments: 0
$$\int\:\frac{\mathrm{sec}\:{x}\:{csc}\:{x}\:{dx}}{\mathrm{ln}\left(\mathrm{tan}\:^{\mathrm{2}} {x}\right)}\:? \\ $$
Question Number 91555 Answers: 1 Comments: 4
Question Number 91542 Answers: 2 Comments: 3
$$\int\:\frac{{x}^{\mathrm{3}} }{\mathrm{2}{x}+\mathrm{1}}\:{dx}\:=\:? \\ $$
Question Number 91534 Answers: 0 Comments: 3
$$\int_{\mathrm{1}} ^{\infty} \frac{{sin}^{\mathrm{2}} \left({x}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$
Question Number 91479 Answers: 1 Comments: 4
$$\:\underset{−\pi/\mathrm{2}\:} {\overset{\pi/\mathrm{2}} {\int}}\:\sqrt{\mathrm{cos}\:{x}−\mathrm{cos}^{\mathrm{3}} {x}}\:\mathrm{dx}=... \\ $$
Question Number 91326 Answers: 2 Comments: 1
Question Number 91310 Answers: 0 Comments: 0
$${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {cot}\:\left({x}\right)\:{ln}\left({sec}\left({x}\right)\right)\:{dx}=\frac{\pi^{\mathrm{2}} }{\mathrm{24}} \\ $$
Question Number 91308 Answers: 0 Comments: 2
$$\int\:\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} −\mathrm{2}}\:{dx}\:? \\ $$
Question Number 91290 Answers: 0 Comments: 1
Question Number 91271 Answers: 1 Comments: 1
$${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{ln}\left(\mathrm{1}+{x}\right)}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$
Question Number 91270 Answers: 0 Comments: 0
$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}+\frac{\mathrm{1}}{{x}}\right)}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx} \\ $$
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