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IntegrationQuestion and Answers: Page 125
Question Number 120285 Answers: 0 Comments: 0
$${calculate}\:\:\int_{\mathrm{2}} ^{\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} \left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)} \\ $$
Question Number 120283 Answers: 0 Comments: 0
$${fond}\:\int_{\mathrm{2}} ^{\infty} \frac{{ln}\left(\mathrm{1}+\mathrm{3}{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{4}} }{dx} \\ $$
Question Number 120257 Answers: 2 Comments: 1
$$\:\int\:\frac{{f}\:'\left({x}\right)}{{f}\left({x}\right)}\:=? \\ $$
Question Number 120254 Answers: 4 Comments: 0
$$\:\int\:\frac{{dx}}{\mathrm{1}+\mathrm{cos}\theta.\mathrm{cos}\:{x}\:}\:? \\ $$
Question Number 120207 Answers: 0 Comments: 0
Question Number 120109 Answers: 0 Comments: 0
Question Number 120102 Answers: 2 Comments: 0
$$\:\Theta\:=\:\int\:\frac{\mathrm{4}{x}^{−\mathrm{1}} +\mathrm{8}{x}^{−\mathrm{3}} }{{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}}}\:{dx}\: \\ $$
Question Number 120064 Answers: 1 Comments: 0
$${I}\:=\:\int\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\:}}\left(\frac{\mathrm{1}}{\mathrm{ln}\:\left(\mathrm{tan}\:{r}\right)}\:+\:\frac{\mathrm{1}}{\mathrm{1}−\mathrm{tan}\:{r}}\:\right)\:{dr} \\ $$
Question Number 120060 Answers: 2 Comments: 0
$$\left({i}\right)\:\underset{−\mathrm{2}} {\overset{\mathrm{0}} {\int}}\:\frac{{dx}}{\mathrm{2}{x}+\mathrm{3}} \\ $$$$\left({ii}\right)\underset{\mathrm{3}} {\overset{\mathrm{5}} {\int}}\:\frac{{dx}}{\:\sqrt[{\mathrm{3}}]{\left(\mathrm{4}−{x}\right)^{\mathrm{2}} }}\: \\ $$
Question Number 120059 Answers: 1 Comments: 0
Question Number 120040 Answers: 2 Comments: 0
$$\:\int\:\frac{{t}^{\mathrm{5}} }{\:\sqrt{\mathrm{2}+{t}^{\mathrm{2}} }}\:{dt}\: \\ $$
Question Number 120025 Answers: 2 Comments: 0
$$\mathrm{calculate}\:\mathrm{f}^{'} \left(\mathrm{x}\right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{f}\left(\mathrm{x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{cos}\left(\mathrm{xt}\right)}{\mathrm{t}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} }\mathrm{dt} \\ $$$$\left.\mathrm{2}\right)\mathrm{f}\left(\mathrm{x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{sin}\left(\mathrm{xt}^{\mathrm{2}} +\sqrt{\mathrm{2}}\right)}{\mathrm{t}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} \:+\mathrm{3}}\mathrm{dt} \\ $$
Question Number 119989 Answers: 2 Comments: 0
Question Number 119970 Answers: 3 Comments: 0
$$\:\int\:\frac{{dx}}{{x}^{\mathrm{2}} \sqrt{\mathrm{25}−{x}^{\mathrm{2}} }}\:? \\ $$
Question Number 119960 Answers: 1 Comments: 0
Question Number 119934 Answers: 2 Comments: 0
$$\:\:\:\int\:\frac{\mathrm{sin}\:^{\mathrm{8}} {x}−\mathrm{cos}\:^{\mathrm{8}} {x}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}{x}}\:{dx}\: \\ $$
Question Number 119930 Answers: 1 Comments: 0
Question Number 119920 Answers: 5 Comments: 0
$$\:\int\:\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}\:{dx}\:=\:?\:,\:{x}\epsilon\left(−\mathrm{1},\mathrm{1}\right) \\ $$
Question Number 119852 Answers: 1 Comments: 0
$$\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{n}^{\mathrm{2}} \:\int\:\underset{\mathrm{0}} {\overset{\frac{\mathrm{1}}{{n}}} {\:}}{x}^{{x}+\mathrm{1}} \:{dx}\:=? \\ $$
Question Number 119784 Answers: 2 Comments: 0
$$\:\:\int\:\frac{{dx}}{\:\sqrt{\left(\mathrm{4}{x}−{x}^{\mathrm{2}} \right)^{\mathrm{3}} }} \\ $$$$ \\ $$
Question Number 119773 Answers: 3 Comments: 0
$$\underset{−\mathrm{4}} {\overset{\mathrm{4}} {\int}}\:{x}^{\mathrm{3}} \sqrt{\mathrm{16}−{x}^{\mathrm{2}} \:}\:\mathrm{sec}\:{x}\:{dx}\: \\ $$
Question Number 119821 Answers: 3 Comments: 0
$$\:\underset{−\mathrm{3}} {\overset{\mathrm{0}} {\int}}\:\frac{\mathrm{6}{x}−\mathrm{6}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}}}\:{dx}\:=? \\ $$
Question Number 119762 Answers: 3 Comments: 0
$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{x}^{\mathrm{4}} \mathrm{dx}}{\left(\mathrm{2x}+\mathrm{1}\right)^{\mathrm{5}} \left(\mathrm{3x}+\mathrm{1}\right)^{\mathrm{8}} } \\ $$
Question Number 119752 Answers: 1 Comments: 0
$${find}\:{I}_{\lambda} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ch}\left(\mathrm{1}+\lambda{cosx}\right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$$\left(\lambda\:{real}\:>\mathrm{0}\right) \\ $$
Question Number 119750 Answers: 1 Comments: 0
$$\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{1019}} {\prod}}\left[\frac{\mathrm{2k}}{\mathrm{2k}−\mathrm{1}}\right]=? \\ $$
Question Number 119696 Answers: 2 Comments: 0
$${For}\:{a}<{b}\:{then}\:\underset{{a}} {\overset{{b}} {\int}}\:\left({x}−{a}\right)\left({x}−{b}\right)\:{dx}\: \\ $$$${equal}\:{to}\:\_ \\ $$
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