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IntegrationQuestion and Answers: Page 25

Question Number 200553 Answers: 0 Comments: 0

∫_0 ^1 ((tan^(−1) (x))/( (√(1+x)))) dx =?

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

Question Number 200474 Answers: 1 Comments: 0

Question Number 200464 Answers: 1 Comments: 0

∫_0 ^(π/2) (dx/(1+tan^(2023) x))=???????

$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\frac{{dx}}{\mathrm{1}+\mathrm{tan}^{\mathrm{2023}} \:{x}}=??????? \\ $$

Question Number 200444 Answers: 1 Comments: 0

Question Number 200403 Answers: 1 Comments: 0

∫ (((x^2 + 1)dx)/(x(x−1)(x+1))) = ??

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

Question Number 200366 Answers: 1 Comments: 1

Question Number 200257 Answers: 1 Comments: 0

Question Number 200256 Answers: 0 Comments: 0

Question Number 200254 Answers: 1 Comments: 0

calculate ... Ω = ∫_(∫_0 ^( (π/2)) ln(tan(x))dx) ^( ∫_0 ^( ∞) ((sin^2 (x))/x^2 ) dx) ln(sin(x))dx=?

$$ \\ $$$$\:\:\:\:\:\:{calculate}\:... \\ $$$$\:\:\Omega\:=\:\int_{\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\mathrm{ln}\left(\mathrm{tan}\left({x}\right)\right){dx}} ^{\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{sin}^{\mathrm{2}} \left({x}\right)}{{x}^{\mathrm{2}} }\:{dx}} \mathrm{ln}\left(\mathrm{sin}\left({x}\right)\right){dx}=? \\ $$

Question Number 200253 Answers: 2 Comments: 0

Question Number 200250 Answers: 2 Comments: 0

Question Number 200159 Answers: 1 Comments: 2

Question Number 200155 Answers: 2 Comments: 0

Question Number 200130 Answers: 2 Comments: 0

solve by contour integrstion ∫_0 ^(2π) (dx/(1+acosx))

$$\:\:{solve}\:{by}\:{contour}\:{integrstion} \\ $$$$\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \frac{{dx}}{\mathrm{1}+{a}\mathrm{cos}{x}}\: \\ $$

Question Number 200048 Answers: 0 Comments: 2

Question Number 200061 Answers: 1 Comments: 0

∫_(−∞) ^(+∞) ((xsinx )/((x^2 +1)(x^2 +4)))dx = ??

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

Question Number 199942 Answers: 1 Comments: 0

Question Number 199934 Answers: 2 Comments: 0

$$\:\:\:\cancel{\underline{\underbrace{ }}\:} \\ $$$$ \\ $$

Question Number 199921 Answers: 1 Comments: 0

Question Number 199907 Answers: 1 Comments: 0

∫ (dx/( (√x) + (x)^(1/3) )) =?

$$\:\:\:\:\:\int\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{x}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{x}}}\:=?\: \\ $$

Question Number 199903 Answers: 2 Comments: 1

∫((x^2 dx)/( (√(x^2 −16)))) = ?

$$\int\frac{{x}^{\mathrm{2}} {dx}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{16}}}\:=\:? \\ $$

Question Number 199598 Answers: 0 Comments: 0

Question Number 199570 Answers: 1 Comments: 0

I = ∫_0 ^(π/2) tan^(−1) (((sinx )/2))dx

$$\:\:\:\:\:\:\:\:\mathrm{I}\:\:\:\:\:=\:\:\:\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{sin}{x}\:}{\mathrm{2}}\right){dx} \\ $$

Question Number 199471 Answers: 1 Comments: 0

Find the integral ∫_(−3) ^3 { ((x^3 −x),((x≤0))),(x^2 ,((x≥0))) :}dx

$${Find}\:{the}\:{integral} \\ $$$$\int_{−\mathrm{3}} ^{\mathrm{3}} \begin{cases}{{x}^{\mathrm{3}} −{x}}&{\left({x}\leq\mathrm{0}\right)}\\{{x}^{\mathrm{2}} }&{\left({x}\geq\mathrm{0}\right)}\end{cases}{dx} \\ $$

Question Number 199468 Answers: 1 Comments: 0

Question Number 199377 Answers: 1 Comments: 0

∫∫_R cos (max{x^3 , y^(3/2) })dx dy , where R = [0,1]×[0,1]

$$\:\:\int\underset{\mathrm{R}} {\int}\mathrm{cos}\:\left(\mathrm{max}\left\{\mathrm{x}^{\mathrm{3}} ,\:\mathrm{y}^{\mathrm{3}/\mathrm{2}} \right\}\right)\mathrm{dx}\:\mathrm{dy}\:,\:\mathrm{where}\:\mathrm{R}\:=\:\left[\mathrm{0},\mathrm{1}\right]×\left[\mathrm{0},\mathrm{1}\right] \\ $$

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