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IntegrationQuestion and Answers: Page 59
Question Number 160597 Answers: 1 Comments: 0
$$\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{dx}}{\mathrm{2}−\mathrm{cos}\:\mathrm{x}}\:=? \\ $$
Question Number 160594 Answers: 1 Comments: 0
$$\:\:\:\:\int\:\frac{\mathrm{dx}}{\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{x}\right)}\:=? \\ $$
Question Number 160590 Answers: 0 Comments: 0
$$ \\ $$$$\:\:\:\:\Omega:=\int_{\mathrm{0}} ^{\:\frac{\mathrm{1}}{\mathrm{2}}} \frac{\:{arcsinh}\left({x}\right)}{{x}}\:{dx}\:\overset{?} {=}\:\frac{\pi^{\mathrm{2}} }{\mathrm{20}} \\ $$
Question Number 160563 Answers: 1 Comments: 0
$$\int\mathrm{x}\left\{\mathrm{x}\right\}\left[\mathrm{x}\right]\mathrm{dx}=? \\ $$
Question Number 160556 Answers: 0 Comments: 0
$$\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{\mathrm{arctg}}\left(\boldsymbol{\mathrm{x}}\right)}{\mathrm{1}+\boldsymbol{\mathrm{x}}}\centerdot\frac{\boldsymbol{\mathrm{dx}}}{\:\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{x}}}}=? \\ $$
Question Number 160551 Answers: 1 Comments: 2
$$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{arctan}\:\mathrm{x}\centerdot\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)\mathrm{dx}=? \\ $$
Question Number 160547 Answers: 1 Comments: 0
$$\:\:{solve} \\ $$$$\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \frac{\:{tan}^{\:−\mathrm{1}} \left(\:{x}\:\right)}{\left(\mathrm{1}+\:{x}^{\:\mathrm{2}} \:\right)\sqrt{\:{x}}}\:{dx}=\:? \\ $$$$−−−−−−−− \\ $$
Question Number 160543 Answers: 0 Comments: 0
$$ \\ $$$$\mathrm{lim}_{\:{x}\rightarrow\:\mathrm{6}} \frac{\:\Gamma\:\left(\:{sin}\left(\:\frac{\pi}{{x}}\right)\right)−\Gamma\:\left(\frac{\mathrm{3}}{{x}}\:\right)}{{sin}\left(\:\pi{x}\:\right)}=\:? \\ $$$$ \\ $$
Question Number 160415 Answers: 1 Comments: 0
$$\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{\mathrm{t}}^{\boldsymbol{\mathrm{n}}} }{\mathrm{1}+\boldsymbol{\mathrm{t}}+\boldsymbol{\mathrm{t}}^{\mathrm{2}} }\boldsymbol{\mathrm{dt}}=? \\ $$
Question Number 160362 Answers: 0 Comments: 0
$$\int\frac{\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{n}}} }{\:\sqrt{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }}\boldsymbol{\mathrm{dx}}=? \\ $$
Question Number 160358 Answers: 1 Comments: 0
$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{ln}\left(\mathrm{sin}{x}\right)\mathrm{ln}\left(\mathrm{cos}{x}\right){dx} \\ $$
Question Number 160349 Answers: 1 Comments: 0
$${find}\:\int\frac{{dx}}{{x}+{e}^{{x}} }=? \\ $$
Question Number 160328 Answers: 0 Comments: 0
$$\:\int_{\mathrm{1}} ^{\:\mathrm{2e}} \:\sqrt{\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}{\mathrm{ln}\:\mathrm{x}}\:\sqrt{\mathrm{ln}\:\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:=? \\ $$
Question Number 160291 Answers: 3 Comments: 0
$$\:\:\:\Omega\:=\:\int\:\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{7}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{4x}+\mathrm{6}\right)^{\mathrm{2}} }\:\mathrm{dx}\:=? \\ $$
Question Number 160281 Answers: 1 Comments: 0
$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{ln}}^{\mathrm{2}} \left(\mathrm{1}−\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{lnx}}}{\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{dx}}=? \\ $$
Question Number 160276 Answers: 1 Comments: 0
$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{ln}}\left(\mathrm{1}−\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}\right)}{\mathrm{1}−\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{dx}}=? \\ $$
Question Number 160204 Answers: 1 Comments: 1
$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{x}}}{\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{3}} }=? \\ $$
Question Number 160194 Answers: 1 Comments: 1
$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{x}}}{\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{6}} }\boldsymbol{\mathrm{dx}}=? \\ $$
Question Number 160113 Answers: 1 Comments: 0
$$ \\ $$$$\:\:{prove}\:\: \\ $$$$\:\:\:\:\:\:\Phi:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{sinh}\left({x}\right)}{{cosh}^{\mathrm{2}} \left({x}\right)}.\frac{\mathrm{1}}{{x}}\:{dx}\:\overset{???} {=}\:\frac{\mathrm{4G}}{\pi} \\ $$
Question Number 160013 Answers: 0 Comments: 1
$$\int\frac{\mathrm{1}}{\mathrm{4}{sin}\:{x}+\mathrm{3}{cos}\:{x}}{dx} \\ $$$${evaluate} \\ $$
Question Number 159960 Answers: 1 Comments: 0
$$\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{3}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{4}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}}}\:{dx}\:=?\: \\ $$
Question Number 159931 Answers: 0 Comments: 0
$$\mathrm{Prove}\:::\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}^{\mathrm{n}} \mathrm{x}}{\mathrm{x}^{\mathrm{m}} }\mathrm{dx}=\frac{\mathrm{1}}{\Gamma\left(\mathrm{m}\right)}\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{D}^{\mathrm{m}−\mathrm{1}} \mathrm{sin}^{\mathrm{n}} \mathrm{x}}{\mathrm{x}}\mathrm{dx} \\ $$$$\mathrm{n}+\mathrm{m}\in\mathrm{Odd}\:\mathrm{Number}. \\ $$
Question Number 159917 Answers: 0 Comments: 1
Question Number 159915 Answers: 0 Comments: 1
$$\:\:\int_{\mathrm{1}} ^{\mathrm{16}} \:\frac{\sqrt{{x}}}{\mathrm{1}+\sqrt[{\mathrm{4}}]{{x}^{\mathrm{3}} }}\:{dx}\:=? \\ $$
Question Number 159870 Answers: 1 Comments: 0
$$\:\:\int\:\frac{\mathrm{1}−\mathrm{cot}\:^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{sin}\:{x}}\:{dx}\:=? \\ $$
Question Number 159823 Answers: 2 Comments: 0
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