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IntegrationQuestion and Answers: Page 125

Question Number 121712 Answers: 1 Comments: 0

Question Number 121707 Answers: 1 Comments: 0

Question Number 121704 Answers: 1 Comments: 0

Question Number 121696 Answers: 2 Comments: 0

∫ ((x^4 −5x^3 +6x^2 −18)/(x^3 −3x^2 )) dx ?

$$\:\:\int\:\frac{{x}^{\mathrm{4}} −\mathrm{5}{x}^{\mathrm{3}} +\mathrm{6}{x}^{\mathrm{2}} −\mathrm{18}}{{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} }\:{dx}\:? \\ $$

Question Number 121680 Answers: 1 Comments: 0

please evaluate ∫x^x dx

$${please}\:{evaluate}\:\int{x}^{{x}} {dx} \\ $$

Question Number 121674 Answers: 3 Comments: 0

... advanced calculus... prove that : Ω =∫_0 ^( ∞) ((sin^4 (x)ln(x))/x^2 )dx=(π/4)(1−γ) γ:euler−mascheroni constant m.n.july.1970

$$\:\:\:\:\:\:\:\:\:...\:\:{advanced}\:\:{calculus}... \\ $$$$\:\:\:\:{prove}\:{that}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\Omega\:=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}^{\mathrm{4}} \left({x}\right){ln}\left({x}\right)}{{x}^{\mathrm{2}} }{dx}=\frac{\pi}{\mathrm{4}}\left(\mathrm{1}−\gamma\right) \\ $$$$\gamma:{euler}−{mascheroni}\:{constant} \\ $$$$\:\:\:\:\:\:{m}.{n}.{july}.\mathrm{1970} \\ $$

Question Number 121611 Answers: 1 Comments: 2

∫_0 ^2 sin (2πx)cos (5πx) dx ?

$$\:\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}\:\mathrm{sin}\:\left(\mathrm{2}\pi\mathrm{x}\right)\mathrm{cos}\:\left(\mathrm{5}\pi\mathrm{x}\right)\:\mathrm{dx}\:?\: \\ $$

Question Number 121602 Answers: 2 Comments: 0

Question Number 121601 Answers: 4 Comments: 0

∫ (dx/(x (√(3+x^2 )))) ?

$$\:\:\int\:\frac{\mathrm{dx}}{\mathrm{x}\:\sqrt{\mathrm{3}+\mathrm{x}^{\mathrm{2}} }}\:? \\ $$

Question Number 121548 Answers: 1 Comments: 0

∫_0 ^(π/4) tan^6 x sec x dx =?

$$\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\mathrm{tan}\:^{\mathrm{6}} \mathrm{x}\:\mathrm{sec}\:\mathrm{x}\:\mathrm{dx}\:=? \\ $$

Question Number 121519 Answers: 1 Comments: 0

∫ ((1−x^4 )/(x^2 (√(x^4 +x^2 +1)))) dx ?

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

Question Number 121498 Answers: 1 Comments: 0

Evaluate Σ_(n=1) ^∞ ((sin(n))/n)

$$ \\ $$$$\mathrm{Evaluate} \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\left(\mathrm{n}\right)}{\mathrm{n}} \\ $$

Question Number 121500 Answers: 3 Comments: 1

(1) ∫ (dx/(x^4 +2x^2 +9)) ? (2) arc tan ((x/3))−arc tan ((x/3))= arc tan ((1/5))

$$\:\left(\mathrm{1}\right)\:\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{4}} +\mathrm{2x}^{\mathrm{2}} +\mathrm{9}}\:? \\ $$$$\left(\mathrm{2}\right)\:\mathrm{arc}\:\mathrm{tan}\:\left(\frac{\mathrm{x}}{\mathrm{3}}\right)−\mathrm{arc}\:\mathrm{tan}\:\left(\frac{\mathrm{x}}{\mathrm{3}}\right)=\:\mathrm{arc}\:\mathrm{tan}\:\left(\frac{\mathrm{1}}{\mathrm{5}}\right) \\ $$

Question Number 121492 Answers: 3 Comments: 0

calculate ∫_0 ^(+∞) (dx/((x^4 +1)^3 ))

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{+\infty} \:\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{3}} } \\ $$

Question Number 121480 Answers: 0 Comments: 0

Question Number 121466 Answers: 1 Comments: 2

∫(√(cos(x) dx))

$$\int\sqrt{{cos}\left({x}\right)\:{dx}} \\ $$

Question Number 121397 Answers: 2 Comments: 0

Question Number 121384 Answers: 2 Comments: 2

∫ (√(1+x^4 )) dx

$$\:\int\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{4}} }\:\mathrm{dx}\: \\ $$

Question Number 121315 Answers: 2 Comments: 0

find lim ∫_(1/n) ^n arctan(1+(x/n))e^(−nx) dx

$${find}\:{lim}\:\int_{\frac{\mathrm{1}}{{n}}} ^{{n}} {arctan}\left(\mathrm{1}+\frac{{x}}{{n}}\right){e}^{−{nx}} {dx} \\ $$

Question Number 121314 Answers: 1 Comments: 0

find lim_(n→+∞) ∫_0 ^n ((cos(nx))/(x^2 +n^2 ))dx

$${find}\:{lim}_{{n}\rightarrow+\infty} \:\int_{\mathrm{0}} ^{{n}} \:\:\:\frac{{cos}\left({nx}\right)}{{x}^{\mathrm{2}} +{n}^{\mathrm{2}} }{dx} \\ $$

Question Number 121300 Answers: 2 Comments: 1

∫ (dx/(x^3 +x^2 +x+1)) ?

$$\:\:\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}\:? \\ $$

Question Number 121225 Answers: 2 Comments: 0

∫_0 ^1 x^5 (√((1+x^2 )/(1−x^2 ))) dx ?

$$\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\mathrm{x}^{\mathrm{5}} \:\sqrt{\frac{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:? \\ $$

Question Number 121224 Answers: 1 Comments: 0

∫ cos^2 x tan^3 x dx

$$\:\:\:\:\int\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{tan}\:^{\mathrm{3}} \mathrm{x}\:\mathrm{dx}\: \\ $$

Question Number 121203 Answers: 2 Comments: 0

∫ ((cos^5 (x))/( (√(sin (x))))) dx

$$\:\int\:\frac{\mathrm{cos}\:^{\mathrm{5}} \left(\mathrm{x}\right)}{\:\sqrt{\mathrm{sin}\:\left(\mathrm{x}\right)}}\:\mathrm{dx}\: \\ $$

Question Number 121174 Answers: 4 Comments: 0

∫_(−π/2) ^(π/2) (x^2 +ln (((π+x)/(π−x))))cos x dx ?

$$\underset{−\pi/\mathrm{2}} {\overset{\pi/\mathrm{2}} {\int}}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{ln}\:\left(\frac{\pi+\mathrm{x}}{\pi−\mathrm{x}}\right)\right)\mathrm{cos}\:\mathrm{x}\:\mathrm{dx}\:? \\ $$

Question Number 121119 Answers: 4 Comments: 0

M= ∫ _(−15) ^(−8) ( (dx/(x(√(1−x))))) ?

$$\mathrm{M}=\:\int\underset{−\mathrm{15}} {\overset{−\mathrm{8}} {\:}}\left(\:\frac{\mathrm{dx}}{\mathrm{x}\sqrt{\mathrm{1}−\mathrm{x}}}\right)\:?\: \\ $$

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