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IntegrationQuestion and Answers: Page 150

Question Number 108841 Answers: 1 Comments: 0

Question Number 108839 Answers: 0 Comments: 1

Question Number 108838 Answers: 0 Comments: 0

Question Number 108821 Answers: 1 Comments: 0

find ∫_0 ^∞ ((lnx)/((x^2 +1)^2 ))dx

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{lnx}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 108789 Answers: 1 Comments: 0

Question Number 108786 Answers: 1 Comments: 0

Question Number 108761 Answers: 2 Comments: 0

((⋮((Be)/(Math))⋮)/★) If ∫_(−1) ^( a) ((x+1)/((x+2)^4 )) = ((10)/(81)) , then the value of a−2 is ___

$$\:\:\:\frac{\vdots\frac{\mathcal{B}{e}}{\mathcal{M}{ath}}\vdots}{\bigstar} \\ $$$${If}\:\int_{−\mathrm{1}} ^{\:\:{a}} \:\frac{{x}+\mathrm{1}}{\left({x}+\mathrm{2}\right)^{\mathrm{4}} }\:=\:\frac{\mathrm{10}}{\mathrm{81}}\:,\:{then}\:{the}\:{value}\:{of} \\ $$$${a}−\mathrm{2}\:{is}\:\_\_\_ \\ $$

Question Number 108750 Answers: 2 Comments: 0

calculste ∫_0 ^∞ ((ln(x))/(x^2 −x+1))dx

$$\mathrm{calculste}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}}\mathrm{dx} \\ $$

Question Number 108749 Answers: 2 Comments: 0

calculste ∫_0 ^∞ ((ln(x))/((1+x)^4 )) dx

$$\mathrm{calculste}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{4}} }\:\mathrm{dx} \\ $$

Question Number 108748 Answers: 1 Comments: 0

Question Number 108738 Answers: 0 Comments: 0

please: ^∗ prove^∗ :::: 1.^(important) lim_(z→1) (ζ (z) −(1/(z−1)) )= γ (euler constant) 2. ^(important) ∫_0 ^( ∞) (cos(x)−(1/(1+x^2 )))(dx/x) =− γ .....M.N.....

$$\:\:\:\:\:\:\:\:{please}:\:\:\:\:\:^{\ast} \mathrm{prove}^{\ast} :::: \\ $$$$\:\:\:\:\:\mathrm{1}.^{\mathrm{important}} \:\:\:\:\mathrm{lim}_{\mathrm{z}\rightarrow\mathrm{1}} \left(\zeta\:\left(\mathrm{z}\right)\:−\frac{\mathrm{1}}{\mathrm{z}−\mathrm{1}}\:\right)=\:\gamma\:\:\:\left(\mathrm{euler}\:\mathrm{constant}\right) \\ $$$$\:\:\:\:\mathrm{2}.\:\overset{\mathrm{important}} {\:}\:\:\int_{\mathrm{0}} ^{\:\infty} \left(\mathrm{cos}\left(\mathrm{x}\right)−\frac{\mathrm{1}}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\right)\frac{\mathrm{dx}}{\mathrm{x}}\:=−\:\gamma \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.....\mathscr{M}.\mathscr{N}..... \\ $$$$\: \\ $$

Question Number 108723 Answers: 2 Comments: 1

Question Number 108710 Answers: 0 Comments: 1

calculate ∫_(−∞) ^∞ (((−1)^x^2 )/((x^2 +x+1)^2 ))dx

$$\mathrm{calculate}\:\:\int_{−\infty} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{\mathrm{x}^{\mathrm{2}} } }{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 108697 Answers: 1 Comments: 0

Question Number 108692 Answers: 2 Comments: 0

Question Number 108667 Answers: 4 Comments: 0

Question Number 108663 Answers: 1 Comments: 0

Question Number 108605 Answers: 2 Comments: 0

((BeMath)/≊) ∫ (x^(11) /((x^8 +1)^2 )) dx

$$\:\:\:\frac{\boldsymbol{{B}}{e}\boldsymbol{{M}}{ath}}{\approxeq} \\ $$$$\:\int\:\frac{{x}^{\mathrm{11}} }{\left({x}^{\mathrm{8}} +\mathrm{1}\right)^{\mathrm{2}} }\:{dx}\: \\ $$

Question Number 108597 Answers: 3 Comments: 0

((∠ BeMath∠)/∦) (1) ∫ cos (ln x) dx (2) ∫ sin (ln x) dx

$$\:\:\:\:\:\frac{\angle\:\mathcal{B}{e}\mathcal{M}{ath}\angle}{\nparallel} \\ $$$$\left(\mathrm{1}\right)\:\int\:\mathrm{cos}\:\left(\mathrm{ln}\:{x}\right)\:{dx}\: \\ $$$$\left(\mathrm{2}\right)\:\int\:\mathrm{sin}\:\left(\mathrm{ln}\:{x}\right)\:{dx}\: \\ $$

Question Number 108593 Answers: 1 Comments: 0

Question Number 108584 Answers: 0 Comments: 0

find ∫_0 ^1 ((ln(1+x^2 ))/(x+2))dx

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}+\mathrm{2}}\mathrm{dx} \\ $$

Question Number 108583 Answers: 1 Comments: 0

find ∫_0 ^1 ((ln(1+x^2 ))/(1+x^2 ))dx

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 108582 Answers: 2 Comments: 0

calculate ∫_0 ^∞ ((ln(1+x))/(1+x^2 )) dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$

Question Number 108573 Answers: 3 Comments: 0

please: in AB^Δ C prove that: ((cos(A))/(sin(B)sin(C))) +((cos(B))/(sin(A)sin(C)))+((cos(C))/(sin(A)sin(B))) =2

$$\:\:\:\:\:\:\:\:\:\mathrm{please}:\:\:\:\mathrm{in}\:\mathrm{A}\overset{\Delta} {\mathrm{B}C}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\:\frac{{cos}\left(\mathrm{A}\right)}{{sin}\left(\mathrm{B}\right){sin}\left(\mathrm{C}\right)}\:+\frac{{cos}\left(\mathrm{B}\right)}{{sin}\left(\mathrm{A}\right){sin}\left(\mathrm{C}\right)}+\frac{{cos}\left(\mathrm{C}\right)}{{sin}\left(\mathrm{A}\right){sin}\left(\mathrm{B}\right)}\:=\mathrm{2}\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 108507 Answers: 1 Comments: 0

∫_0 ^(π/6) (√((3cos2x−1)/(cos^2 (x)))) dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{6}}} \sqrt{\frac{\mathrm{3}{cos}\mathrm{2}{x}−\mathrm{1}}{{cos}^{\mathrm{2}} \left({x}\right)}}\:{dx} \\ $$

Question Number 108506 Answers: 1 Comments: 0

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