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IntegrationQuestion and Answers: Page 192

Question Number 86013 Answers: 0 Comments: 1

calculate ∫_(1+(√2)) ^(+∞) (dx/((x−1)^3 (x+2)^3 ))

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

Question Number 85999 Answers: 0 Comments: 5

∫_0 ^∞ ((sinx^2 )/(1+x^4 ))dx=0.4009 prove that

$$\int_{\mathrm{0}} ^{\infty} \frac{{sinx}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{4}} }{dx}=\mathrm{0}.\mathrm{4009} \\ $$$${prove}\:{that} \\ $$

Question Number 85952 Answers: 1 Comments: 0

∫ ((√x)/(2+(x)^(1/(3 )) )) dx

$$\int\:\:\frac{\sqrt{\mathrm{x}}}{\mathrm{2}+\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}}}\:\mathrm{dx}\: \\ $$

Question Number 85914 Answers: 1 Comments: 0

Let I_n =∫_(0 ) ^(π/4) (((1−tan A)/(1+tan A)))^n dA what is the Laplace Transform and the Fourier Transform

$${Let}\:{I}_{{n}} =\overset{\pi/\mathrm{4}} {\int}_{\mathrm{0}\:} \left(\frac{\mathrm{1}−\mathrm{tan}\:{A}}{\mathrm{1}+\mathrm{tan}\:{A}}\right)^{{n}} {dA}\:\:{what}\:{is} \\ $$$${the}\:{Laplace}\:{Transform}\:{and}\:{the} \\ $$$${Fourier}\:{Transform} \\ $$

Question Number 85909 Answers: 2 Comments: 2

∫ sin^(−1) ((√(x/(a+x)))) dx , a > 0

$$\int\:\mathrm{sin}^{−\mathrm{1}} \:\left(\sqrt{\frac{\mathrm{x}}{\mathrm{a}+\mathrm{x}}}\right)\:\mathrm{dx}\:,\:\mathrm{a}\:>\:\mathrm{0} \\ $$

Question Number 85896 Answers: 2 Comments: 4

Question Number 85890 Answers: 0 Comments: 0

Is there a sum for ψ((p/q)) or an integral for any fraction p/q

$${Is}\:{there}\:{a}\:{sum}\:{for}\:\psi\left(\frac{{p}}{{q}}\right)\:{or}\:{an}\:{integral} \\ $$$${for}\:{any}\:{fraction}\:{p}/{q} \\ $$

Question Number 85875 Answers: 1 Comments: 0

∫((1/(7[1−(1/7)e^x ]))) dx

$$\int\left(\frac{\mathrm{1}}{\mathrm{7}\left[\mathrm{1}−\frac{\mathrm{1}}{\mathrm{7}}\mathrm{e}^{\mathrm{x}} \right]}\right)\:\mathrm{dx} \\ $$

Question Number 85839 Answers: 1 Comments: 1

∫x×(1/(√(x^2 −1)))dx

$$\int\mathrm{x}×\frac{\mathrm{1}}{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}}\mathrm{dx} \\ $$

Question Number 85828 Answers: 1 Comments: 0

∫(1/(x+cot(x))) dx

$$\int\frac{\mathrm{1}}{{x}+{cot}\left({x}\right)}\:{dx} \\ $$

Question Number 85807 Answers: 1 Comments: 0

∫_0 ^1 ((x^2 dx)/(√(1−x^4 )))

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{x}^{\mathrm{2}} \:\mathrm{dx}}{\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }} \\ $$

Question Number 85801 Answers: 0 Comments: 3

calculate ∫_0 ^π (dx/((cosx +2sinx)^2 ))

$${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dx}}{\left({cosx}\:+\mathrm{2}{sinx}\right)^{\mathrm{2}} } \\ $$

Question Number 85793 Answers: 0 Comments: 0

∫_1 ^2 ((tan^(−1) (x−1) ln(x−1))/x) dx

$$\int_{\mathrm{1}} ^{\mathrm{2}} \frac{{tan}^{−\mathrm{1}} \left({x}−\mathrm{1}\right)\:{ln}\left({x}−\mathrm{1}\right)}{{x}}\:{dx} \\ $$

Question Number 85789 Answers: 1 Comments: 0

∫(ln x)^2 dx =

$$\int\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}} \:{dx}\:= \\ $$

Question Number 85781 Answers: 1 Comments: 2

∫_0 ^1 (ln (1/x))^(−3/2) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \:\left(\mathrm{ln}\:\frac{\mathrm{1}}{{x}}\right)^{−\mathrm{3}/\mathrm{2}} \:{dx} \\ $$

Question Number 85776 Answers: 1 Comments: 0

Question Number 85775 Answers: 0 Comments: 0

Question Number 85760 Answers: 0 Comments: 0

∫(([cos^(−1) (x){(√(1−x^2 ))}]^(−1) )/(log{((sin(2x(√(1−x^2 ))))/π)})) dx

$$\int\frac{\left[{cos}^{−\mathrm{1}} \left({x}\right)\left\{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right\}\right]^{−\mathrm{1}} }{{log}\left\{\frac{{sin}\left(\mathrm{2}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right)}{\pi}\right\}}\:{dx} \\ $$

Question Number 85721 Answers: 1 Comments: 0

show that ∫_0 ^∞ ((e^(−x) ln(x))/(√x))dx=−(√π)(γ+ln(4))

$${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{e}^{−{x}} {ln}\left({x}\right)}{\sqrt{{x}}}{dx}=−\sqrt{\pi}\left(\gamma+{ln}\left(\mathrm{4}\right)\right) \\ $$

Question Number 85718 Answers: 1 Comments: 0

∫((sin(x)−cos(3x))/(sin(x)−cos(2x)))dx

$$\int\frac{{sin}\left({x}\right)−{cos}\left(\mathrm{3}{x}\right)}{{sin}\left({x}\right)−{cos}\left(\mathrm{2}{x}\right)}{dx} \\ $$

Question Number 85717 Answers: 1 Comments: 0

∫_0 ^2 x^4 (√(1−x^2 )) dx ∫_0 ^1 x^(10) (1−x^n )dx

$$\int_{\mathrm{0}} ^{\mathrm{2}} {x}^{\mathrm{4}} \sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:{dx} \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{10}} \left(\mathrm{1}−{x}^{{n}} \right){dx} \\ $$$$ \\ $$

Question Number 85711 Answers: 0 Comments: 2

∫_(−4) ^2 ((2x + 1)/((x^2 + x + 1)^(3/2) )) dx

$$\:\underset{−\mathrm{4}} {\overset{\mathrm{2}} {\int}}\:\frac{\mathrm{2}{x}\:+\:\mathrm{1}}{\left({x}^{\mathrm{2}} +\:{x}\:+\:\mathrm{1}\right)^{\mathrm{3}/\mathrm{2}} }\:{dx} \\ $$

Question Number 85701 Answers: 1 Comments: 3

∫ ((√(3x−1))/(√(2x+1))) dx

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

Question Number 85677 Answers: 2 Comments: 3

∫_0 ^π ((sin (((21x)/2)))/(sin ((x/2)))) dx

$$\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{\mathrm{sin}\:\left(\frac{\mathrm{21}{x}}{\mathrm{2}}\right)}{\mathrm{sin}\:\left(\frac{{x}}{\mathrm{2}}\right)}\:{dx}\: \\ $$

Question Number 85669 Answers: 1 Comments: 4

∫ ((√(1+x))/(√(1−x))) dx

$$\int\:\frac{\sqrt{\mathrm{1}+{x}}}{\sqrt{\mathrm{1}−{x}}}\:{dx} \\ $$$$ \\ $$

Question Number 85667 Answers: 1 Comments: 0

∫ (dx/(√(1−sin 2x)))

$$\int\:\frac{{dx}}{\sqrt{\mathrm{1}−\mathrm{sin}\:\mathrm{2}{x}}}\: \\ $$

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