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Question Number 65405 Answers: 0 Comments: 1

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1) calculate ∫_0 ^∞ (dx/(1+e^(nx) )) with n integr natural and n≥1 2) conclude the value of Σ_(k=1) ^∞ (((−1)^(k−1) )/k)

$$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\mathrm{1}+{e}^{{nx}} }\:\:\:{with}\:{n}\:{integr}\:{natural}\:\:{and}\:{n}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{conclude}\:{the}\:{value}\:{of}\:\sum_{{k}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{k}−\mathrm{1}} }{{k}} \\ $$

Question Number 65380 Answers: 1 Comments: 1

Question Number 65387 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((arctan(2x)−arctanx)/x)dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left(\mathrm{2}{x}\right)−{arctanx}}{{x}}{dx} \\ $$

Question Number 65386 Answers: 0 Comments: 1

calculate Σ_(k=1) ^∞ (((−1)^(k−1) )/(99k−1))

$${calculate}\:\sum_{{k}=\mathrm{1}} ^{\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{k}−\mathrm{1}} }{\mathrm{99}{k}−\mathrm{1}} \\ $$

Question Number 65372 Answers: 0 Comments: 4

I=∫_1 ^e (dx/(x(1+ln^2 x)))

$${I}=\int_{\mathrm{1}} ^{{e}} \:\frac{{dx}}{{x}\left(\mathrm{1}+{ln}^{\mathrm{2}} {x}\right)} \\ $$

Question Number 65367 Answers: 2 Comments: 1

Question Number 65366 Answers: 2 Comments: 2

Question Number 65365 Answers: 2 Comments: 0

3sinA+4cosB=6 3cosA+4sinB=1 find angle C

$$\mathrm{3sinA}+\mathrm{4cosB}=\mathrm{6} \\ $$$$\mathrm{3cosA}+\mathrm{4sinB}=\mathrm{1} \\ $$$$\mathrm{find}\:\mathrm{angle}\:\mathrm{C} \\ $$

Question Number 65359 Answers: 0 Comments: 0

φφ

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Question Number 65356 Answers: 1 Comments: 1

Question Number 65355 Answers: 2 Comments: 1

find ∫ (dx/(√((x+1)(x+2)(x+3))))

$${find}\:\int\:\:\:\frac{{dx}}{\sqrt{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)}} \\ $$

Question Number 65354 Answers: 0 Comments: 3

find ∫ (dx/(√(x^2 +x−2)))

$${find}\:\:\int\:\:\:\:\:\:\frac{{dx}}{\sqrt{{x}^{\mathrm{2}} +{x}−\mathrm{2}}} \\ $$$$ \\ $$

Question Number 65352 Answers: 0 Comments: 1

give the integralA_n = ∫_1 ^(+∞) (dt/(1+x^n )) with n integr and n≥2 at form of serie.

$${give}\:{the}\:{integralA}_{{n}} =\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{dt}}{\mathrm{1}+{x}^{{n}} }\:\:{with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{2} \\ $$$${at}\:{form}\:{of}\:{serie}. \\ $$

Question Number 65347 Answers: 1 Comments: 0

Question Number 65345 Answers: 1 Comments: 4

find the maximum value of sin^(2018) x +cos^(2019) x ?

$$\mathrm{find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{sin}^{\mathrm{2018}} \mathrm{x}\:+\mathrm{cos}^{\mathrm{2019}} \mathrm{x}\:? \\ $$

Question Number 65335 Answers: 0 Comments: 0

Question Number 65334 Answers: 1 Comments: 0

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Question Number 65333 Answers: 1 Comments: 1

Question Number 65314 Answers: 0 Comments: 1

Question Number 65312 Answers: 0 Comments: 2

Question Number 65307 Answers: 1 Comments: 0

∫(((4x+3)dx)/(√(2x^2 +2x−3))) = ?

$$\int\frac{\left(\mathrm{4}{x}+\mathrm{3}\right){dx}}{\sqrt{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{3}}}\:=\:?\: \\ $$

Question Number 65325 Answers: 1 Comments: 3

Question Number 65324 Answers: 0 Comments: 3

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