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IntegrationQuestion and Answers: Page 187

Question Number 88071 Answers: 1 Comments: 7

Question Number 88069 Answers: 1 Comments: 2

Question Number 88064 Answers: 1 Comments: 0

∫ (dx/(cos x(2+sin x)))?

$$\int\:\frac{\mathrm{dx}}{\mathrm{cos}\:\mathrm{x}\left(\mathrm{2}+\mathrm{sin}\:\mathrm{x}\right)}? \\ $$

Question Number 88045 Answers: 0 Comments: 2

∫ ((sin x)/(2sin x+cos x)) dx

$$\int\:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{2sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}}\:\mathrm{dx}\: \\ $$

Question Number 88042 Answers: 1 Comments: 0

find max and min value of function f(x) = (5/(−3cos x−4sin x))

$$\mathrm{find}\:\mathrm{max}\:\mathrm{and}\:\mathrm{min}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{5}}{−\mathrm{3cos}\:\mathrm{x}−\mathrm{4sin}\:\mathrm{x}} \\ $$

Question Number 88033 Answers: 0 Comments: 4

find ∫_0 ^1 ((sin(x))/x)dx

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

Question Number 88026 Answers: 0 Comments: 0

Question Number 88010 Answers: 0 Comments: 2

∫((x^2 +2x+3)/(√(x^2 +x+1)))dx

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

Question Number 88007 Answers: 1 Comments: 0

∫_0 ^1 (√((√((4/x)−3))−1))dx=?

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\sqrt{\sqrt{\frac{\mathrm{4}}{{x}}−\mathrm{3}}−\mathrm{1}}{dx}=? \\ $$

Question Number 88003 Answers: 0 Comments: 2

Determine all functions f[0,1]→Ω such that ∀x∈[0,1] f ′(x)+f(x)=f(0)+f(1)

$${Determine}\:{all}\:{functions}\:{f}\left[\mathrm{0},\mathrm{1}\right]\rightarrow\Omega \\ $$$${such}\:{that}\:\forall{x}\in\left[\mathrm{0},\mathrm{1}\right]\:{f}\:'\left({x}\right)+{f}\left({x}\right)={f}\left(\mathrm{0}\right)+{f}\left(\mathrm{1}\right) \\ $$

Question Number 87996 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((arctan(3x)−arctanx)/x)dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{3}{x}\right)−{arctanx}}{{x}}{dx} \\ $$

Question Number 87995 Answers: 1 Comments: 0

find ∫ (dx/((x^2 −1)^2 (x^2 +2)))

$${find}\:\int\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} \left({x}^{\mathrm{2}} \:+\mathrm{2}\right)} \\ $$

Question Number 87994 Answers: 0 Comments: 0

vcalculate ∫_0 ^∞ ((arctan(2[x]+3))/(x^2 +9))dx

$${vcalculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{2}\left[{x}\right]+\mathrm{3}\right)}{{x}^{\mathrm{2}} \:+\mathrm{9}}{dx} \\ $$

Question Number 87993 Answers: 0 Comments: 1

calculate ∫_0 ^∞ (dx/((x+1)^2 (x+2)^2 (x+3)^2 ))

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} \left({x}+\mathrm{2}\right)^{\mathrm{2}} \left({x}+\mathrm{3}\right)^{\mathrm{2}} } \\ $$

Question Number 87977 Answers: 0 Comments: 2

∫_(−(π/2)) ^(π/2) ((sin 2x)/(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 87969 Answers: 1 Comments: 0

Question Number 87930 Answers: 0 Comments: 0

Question Number 87920 Answers: 0 Comments: 1

Question Number 87910 Answers: 0 Comments: 0

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Question Number 87903 Answers: 0 Comments: 0

find ∫_0 ^∞ ∫_0 ^∞ ((arctan(xy))/((x+y)^2 ))dxdy

$${find}\:\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left({xy}\right)}{\left({x}+{y}\right)^{\mathrm{2}} }{dxdy} \\ $$

Question Number 87902 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ∫_0 ^∞ (e^(−(x^2 +y^2 )) /((x+y)^2 ))dxdy

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \frac{{e}^{−\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)} }{\left({x}+{y}\right)^{\mathrm{2}} }{dxdy} \\ $$

Question Number 87901 Answers: 0 Comments: 0

calculate ∫∫_([0,1]^2 ) ((arctan(x+y))/(x+y))dxdy

$${calculate}\:\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} } \:\:\:\frac{{arctan}\left({x}+{y}\right)}{{x}+{y}}{dxdy} \\ $$

Question Number 87893 Answers: 1 Comments: 0

∫ (√((sin x)/(sin x−cos x))) dx

$$\int\:\sqrt{\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}}}\:\:\mathrm{dx}\: \\ $$

Question Number 87881 Answers: 1 Comments: 1

∫_(−∞) ^( +∞) (1/x) dx =

$$\:\int_{−\infty} ^{\:+\infty} \frac{\mathrm{1}}{{x}}\:{dx}\:=\: \\ $$

Question Number 87876 Answers: 0 Comments: 1

prove that Γ(z)=∫_0 ^∞ e^(−x) x^(z−1) dx,Re(z)>0

$${prove}\:{that} \\ $$$$\Gamma\left({z}\right)=\int_{\mathrm{0}} ^{\infty} {e}^{−{x}} \:{x}^{{z}−\mathrm{1}} \:{dx},{Re}\left({z}\right)>\mathrm{0} \\ $$

Question Number 87839 Answers: 1 Comments: 0

I = ∫_0 ^(π/4) ((sin 4x)/(cos^2 x (√(tan^4 x+1)))) dx

$$\mathrm{I}\:=\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{4}}} {\int}}\:\frac{\mathrm{sin}\:\mathrm{4x}}{\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\sqrt{\mathrm{tan}\:^{\mathrm{4}} \mathrm{x}+\mathrm{1}}}\:\mathrm{dx} \\ $$

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