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AllQuestion and Answers: Page 31

Question Number 222730 Answers: 2 Comments: 1

Question Number 222736 Answers: 1 Comments: 0

Question Number 222718 Answers: 2 Comments: 3

Question Number 222711 Answers: 1 Comments: 0

Question Number 222705 Answers: 2 Comments: 0

∫_0 ^1 ((lnxarctanx)/x)dx

$$\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}{x}\mathrm{arctan}{x}}{{x}}{dx} \\ $$

Question Number 222703 Answers: 1 Comments: 1

Question Number 222697 Answers: 1 Comments: 0

Question Number 222685 Answers: 2 Comments: 0

Question Number 222684 Answers: 1 Comments: 1

Question Number 222679 Answers: 2 Comments: 0

If x=Π_(x=1) ^(10) x then (1/(log _2 x))+(1/(log _3 x))+(1/(log _4 x))...+(1/(log _(10) x))=??

$${If}\:{x}=\underset{{x}=\mathrm{1}} {\overset{\mathrm{10}} {\prod}}{x}\:{then}\:\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{2}} {x}}+\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{3}} {x}}+\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{4}} {x}}...+\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{10}} {x}}=?? \\ $$

Question Number 222673 Answers: 1 Comments: 1

Question Number 222662 Answers: 1 Comments: 4

Question Number 222652 Answers: 0 Comments: 1

Question Number 222646 Answers: 2 Comments: 0

Question Number 222639 Answers: 2 Comments: 0

Question Number 222638 Answers: 1 Comments: 0

Question Number 222636 Answers: 3 Comments: 0

Question Number 222635 Answers: 1 Comments: 0

Question Number 222622 Answers: 0 Comments: 0

Question Number 222619 Answers: 2 Comments: 0

Question Number 222614 Answers: 0 Comments: 0

complicated solution of the integral ; ∫ tan(((cos x)/x))^(13) dx

$$ \\ $$$$\:\:\mathrm{complicated}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integral}\:; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\mathrm{tan}\left(\frac{\mathrm{cos}\:{x}}{{x}}\right)^{\mathrm{13}} \:\mathrm{d}{x} \\ $$$$ \\ $$

Question Number 222613 Answers: 0 Comments: 0

what is I = ∫ tan (((cos x)/x)) dx

$$ \\ $$$$\:\:\:\:\:\:\mathrm{what}\:\mathrm{is}\:\:{I}\:=\:\int\:\mathrm{tan}\:\left(\frac{\mathrm{cos}\:{x}}{{x}}\right)\:\mathrm{d}{x}\: \\ $$$$ \\ $$

Question Number 222616 Answers: 1 Comments: 0

Question Number 222610 Answers: 0 Comments: 0

Σ_(n=1) ^∞ (1/(n(e^(2πn) − 1)))

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{n}\left({e}^{\mathrm{2}\pi{n}} \:−\:\mathrm{1}\right)} \\ $$$$ \\ $$

Question Number 222624 Answers: 1 Comments: 0

Question Number 222607 Answers: 1 Comments: 0

Prove:∫_0 ^1 (x^3 /(5−x^3 ))∙(1/( ((1−x^3 ))^(1/3) ))dx=((((10))^(1/3) −2)/(3(√3)))π

$$\mathrm{Prove}:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{3}} }{\mathrm{5}−{x}^{\mathrm{3}} }\centerdot\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{1}−{x}^{\mathrm{3}} }}{dx}=\frac{\sqrt[{\mathrm{3}}]{\mathrm{10}}−\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}}\pi \\ $$

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