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IntegrationQuestion and Answers: Page 130

Question Number 117342 Answers: 2 Comments: 0

(1)∫ (tan^(−1) (x))^2 dx = ? (2) ∫ tan^(−1) ((√x)) dx =?

$$\:\left(\mathrm{1}\right)\int\:\left(\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)\right)^{\mathrm{2}} \:\mathrm{dx}\:=\:? \\ $$$$\left(\mathrm{2}\right)\:\int\:\mathrm{tan}^{−\mathrm{1}} \left(\sqrt{\mathrm{x}}\right)\:\mathrm{dx}\:=? \\ $$

Question Number 117329 Answers: 1 Comments: 0

nice math evaluate:: Ω=∫_0 ^( 1) ((arctan(x).ln(1−x))/(1+x^2 ))dx??? m.n.1970

$$\:\:\:\:\:\:\:\:\:{nice}\:\:{math} \\ $$$$\:\:{evaluate}:: \\ $$$$ \\ $$$$\:\:\:\: \\ $$$$\:\: \\ $$$$ \\ $$$$\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{arctan}\left({x}\right).{ln}\left(\mathrm{1}−{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}??? \\ $$$$\:\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$$$ \\ $$

Question Number 117311 Answers: 2 Comments: 0

Question Number 117253 Answers: 3 Comments: 0

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

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

Question Number 117249 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (((−1)^x^2 )/(x^4 +x^2 +1))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{\mathrm{x}^{\mathrm{2}} } }{\mathrm{x}^{\mathrm{4}} \:+\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}}\mathrm{dx}\: \\ $$

Question Number 117227 Answers: 0 Comments: 0

why every function that is Riemann integrable is not lebsgue integrable?

$${why}\:{every}\:{function}\:{that}\:{is}\:{Riemann} \\ $$$${integrable}\:{is}\:{not}\:{lebsgue}\:{integrable}? \\ $$

Question Number 117221 Answers: 3 Comments: 1

∫_(−∞) ^( ∞) ((cos (3x))/(x^2 +4)) dx =?

$$\underset{−\infty} {\overset{\:\:\:\:\:\infty} {\int}}\:\frac{\mathrm{cos}\:\left(\mathrm{3}{x}\right)}{{x}^{\mathrm{2}} +\mathrm{4}}\:{dx}\:=? \\ $$

Question Number 117176 Answers: 4 Comments: 1

∫_(π/4) ^(π/2) ((4cot x+1 )/(4−cot x)) dx =?

$$\underset{\pi/\mathrm{4}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\mathrm{4cot}\:{x}+\mathrm{1}\:}{\mathrm{4}−\mathrm{cot}\:{x}}\:{dx}\:=? \\ $$

Question Number 117163 Answers: 2 Comments: 0

∫ ((4 dx)/(x (√(x^2 −1)))) =?

$$\:\:\:\int\:\frac{\mathrm{4}\:\mathrm{dx}}{\mathrm{x}\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}}\:=? \\ $$

Question Number 117213 Answers: 3 Comments: 0

∫_0 ^( ∞) ((tan^(−1) ((x/4))−tan^(−1) ((x/6)))/x) dx =?

$$\:\:\underset{\mathrm{0}} {\overset{\:\:\:\:\:\:\:\infty} {\int}}\:\frac{\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{x}}{\mathrm{4}}\right)−\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{x}}{\mathrm{6}}\right)}{\mathrm{x}}\:\mathrm{dx}\:=? \\ $$

Question Number 117100 Answers: 3 Comments: 0

∫ sin^6 (2x) cos^6 (2x) dx =?

$$\int\:\mathrm{sin}\:^{\mathrm{6}} \left(\mathrm{2x}\right)\:\mathrm{cos}\:^{\mathrm{6}} \left(\mathrm{2x}\right)\:\mathrm{dx}\:=? \\ $$

Question Number 117148 Answers: 2 Comments: 0

∫ x^6 e^(−4x^2 ) dx =?

$$\:\:\:\int\:\mathrm{x}^{\mathrm{6}} \:\mathrm{e}^{−\mathrm{4x}^{\mathrm{2}} } \:\mathrm{dx}\:=? \\ $$

Question Number 117090 Answers: 0 Comments: 0

Question Number 117089 Answers: 0 Comments: 0

Question Number 117088 Answers: 2 Comments: 0

... advanced calculus... evsluate :: I=∫_0 ^( ∞) ((xsin(2x))/(x^2 +4)) dx =? hint: Φ=∫_0 ^( ∞) ((cos(px))/(x^2 +1))dx =(π/2)e^(−p) (p>0) .m.n 1970

$$\:\:\:\:\:\:\:\:\:\:...\:{advanced}\:\:\:{calculus}... \\ $$$$ \\ $$$$\:\:\:\:\:\:\:{evsluate}\::: \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\mathrm{I}=\int_{\mathrm{0}} ^{\:\infty} \frac{{xsin}\left(\mathrm{2}{x}\right)}{{x}^{\mathrm{2}} +\mathrm{4}}\:{dx}\:=? \\ $$$$\:\:\:\:\:{hint}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\Phi=\int_{\mathrm{0}} ^{\:\infty} \frac{{cos}\left({px}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}{dx}\:=\frac{\pi}{\mathrm{2}}{e}^{−{p}} \:\:\:\:\left({p}>\mathrm{0}\right)\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:.{m}.{n}\:\mathrm{1970} \\ $$$$ \\ $$

Question Number 117087 Answers: 2 Comments: 0

... nice calculus... please evaluate :: Ω=∫_0 ^( 1) ((x^4 +1)/(x^6 +1))dx =??? m.n.1970

$$\:\:\:\:\:\:\:\:\:...\:\:{nice}\:\:{calculus}... \\ $$$$\:{please}\:\:{evaluate}\::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{x}^{\mathrm{4}} +\mathrm{1}}{{x}^{\mathrm{6}} +\mathrm{1}}{dx}\:=??? \\ $$$$\:\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$

Question Number 117066 Answers: 1 Comments: 0

Given f(x)= ((x−1)/(x+1)) . If f^2 (x)=f(f(x)), f^3 (x)=f(f(f(x))) , f^(1998) (x) = g(x) then ∫_(1/e) ^1 g(x) dx = _?

Question Number 117053 Answers: 4 Comments: 0

∫ (x/( (√(2−x^4 )))) dx =?

$$\:\:\:\int\:\frac{\mathrm{x}}{\:\sqrt{\mathrm{2}−\mathrm{x}^{\mathrm{4}} }}\:\mathrm{dx}\:=? \\ $$

Question Number 117121 Answers: 2 Comments: 0

...nice mathematics.. please evaluate... Ω =∫_(−∞) ^( +∞) (((x^2 −4)/(x^2 +4))∗ ((sin(2x))/x)) dx =??? m.n.1970

$$\:\:\:\:\:\:\:\:...{nice}\:\:{mathematics}.. \\ $$$$ \\ $$$$\:\:{please}\:\:{evaluate}... \\ $$$$\: \\ $$$$\:\Omega\:=\int_{−\infty} ^{\:+\infty} \left(\frac{{x}^{\mathrm{2}} −\mathrm{4}}{{x}^{\mathrm{2}} +\mathrm{4}}\ast\:\frac{{sin}\left(\mathrm{2}{x}\right)}{{x}}\right)\:{dx}\:=???\:\: \\ $$$$\:{m}.{n}.\mathrm{1970} \\ $$$$ \\ $$

Question Number 117034 Answers: 1 Comments: 0

∫(dx/( ((1+x^3 ))^(1/3) ))

$$\int\frac{\boldsymbol{\mathrm{dx}}}{\:\sqrt[{\mathrm{3}}]{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{3}} }} \\ $$

Question Number 117006 Answers: 2 Comments: 1

∫_0 ^(100π) ∣sinx∣ dx

$$\int_{\mathrm{0}} ^{\mathrm{100}\pi} \mid{sinx}\mid\:{dx} \\ $$

Question Number 117002 Answers: 1 Comments: 0

∫_0 ^(nπ+v) ∣sinx∣ dx

$$\int_{\mathrm{0}} ^{{n}\pi+{v}} \mid{sinx}\mid\:{dx} \\ $$

Question Number 116999 Answers: 3 Comments: 0

∫(dx/((a+bcosx)^2 ))

$$\int\frac{{dx}}{\left({a}+{bcosx}\right)^{\mathrm{2}} } \\ $$

Question Number 116998 Answers: 2 Comments: 2

∫_((−π)/2) ^(π/2) ((sin^2 x)/(1+2^x ))dx

$$\int_{\frac{−\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{sin}^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{2}^{{x}} }{dx} \\ $$

Question Number 116996 Answers: 2 Comments: 0

Question Number 116903 Answers: 2 Comments: 0

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