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Question Number 68598 Answers: 0 Comments: 2

find ∫ (dx/(x^3 −4x +3))

$$\:{find}\:\int\:\:\:\:\frac{{dx}}{{x}^{\mathrm{3}} −\mathrm{4}{x}\:+\mathrm{3}} \\ $$

Question Number 68597 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((arctan(e^x^2 ))/(x^2 +8))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left({e}^{{x}^{\mathrm{2}} } \right)}{{x}^{\mathrm{2}} \:+\mathrm{8}}{dx} \\ $$

Question Number 68596 Answers: 0 Comments: 1

calculate ∫_(π/2) ^(π/3) ((xdx)/(3+cosx))

$${calculate}\:\int_{\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{3}}} \:\:\:\:\frac{{xdx}}{\mathrm{3}+{cosx}} \\ $$

Question Number 68595 Answers: 0 Comments: 1

calculate A_λ =∫_0 ^∞ (e^(−λx^2 ) /(x^4 +1))dx with λ>0 and find ∫_0 ^1 A_λ dλ

$${calculate}\:\:{A}_{\lambda} =\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{e}^{−\lambda{x}^{\mathrm{2}} } }{{x}^{\mathrm{4}} +\mathrm{1}}{dx}\:\:{with}\:\lambda>\mathrm{0}\:\:{and}\: \\ $$$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{A}_{\lambda} \:{d}\lambda \\ $$

Question Number 68594 Answers: 0 Comments: 0

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

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

Question Number 68593 Answers: 0 Comments: 1

calculate Σ_(n=1) ^∞ (((−1)^n )/(n(2n+1)^2 ))

$${calculate}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 68592 Answers: 0 Comments: 2

find Σ_(n=1) ^∞ (1/(n^2 (n+1)^3 ))

$${find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$

Question Number 68591 Answers: 0 Comments: 6

Question Number 68589 Answers: 1 Comments: 0

Question Number 68632 Answers: 0 Comments: 0

(sin(π/9) + i sin((3π)/(18)))^(−9)

$$\left({sin}\frac{\pi}{\mathrm{9}}\:+\:{i}\:{sin}\frac{\mathrm{3}\pi}{\mathrm{18}}\right)^{−\mathrm{9}} \\ $$

Question Number 68554 Answers: 0 Comments: 4

Question Number 68549 Answers: 1 Comments: 3

y=(x^3 /(x^2 +1)) y^(−1) =...

$${y}=\frac{{x}^{\mathrm{3}} }{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$${y}^{−\mathrm{1}} =... \\ $$

Question Number 68546 Answers: 1 Comments: 0

find the range and domain of f(x) f(x)=(√(sin^(−1) (ln(x/(10)))))

$${find}\:{the}\:{range}\:{and}\:{domain}\:{of}\:{f}\left({x}\right) \\ $$$$ \\ $$$${f}\left({x}\right)=\sqrt{{sin}^{−\mathrm{1}} \left({ln}\frac{{x}}{\mathrm{10}}\right)} \\ $$

Question Number 68541 Answers: 1 Comments: 1

Question Number 68537 Answers: 2 Comments: 0

Question Number 68532 Answers: 0 Comments: 0

Question Number 68521 Answers: 0 Comments: 1

lim_(x→0) ((4 sin x + 2 tan x − 6x)/x^5 ) = ? Without L′Hospital

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{4}\:\mathrm{sin}\:{x}\:+\:\mathrm{2}\:\mathrm{tan}\:{x}\:−\:\mathrm{6}{x}}{{x}^{\mathrm{5}} }\:\:=\:\:? \\ $$$${Without}\:\:{L}'{Hospital} \\ $$

Question Number 68517 Answers: 0 Comments: 0

Question Number 68515 Answers: 1 Comments: 2

Question Number 68510 Answers: 1 Comments: 0

Question Number 68509 Answers: 0 Comments: 0

Question Number 68508 Answers: 0 Comments: 0

Question Number 68506 Answers: 0 Comments: 0

y′=4y^2 +x^2 +1 what the primitive solution

$${y}'=\mathrm{4}{y}^{\mathrm{2}} +{x}^{\mathrm{2}} +\mathrm{1} \\ $$$${what}\:{the}\:{primitive}\:{solution} \\ $$

Question Number 68503 Answers: 0 Comments: 8

Question Number 68524 Answers: 1 Comments: 0

Question Number 68528 Answers: 0 Comments: 0

lim_(t→∞) [(1/t) ∫_1 ^( t) (t)^(1/x) dx]

$$\underset{{t}\rightarrow\infty} {\mathrm{lim}}\:\left[\frac{\mathrm{1}}{{t}}\:\int_{\mathrm{1}} ^{\:{t}} \:\sqrt[{{x}}]{{t}}\:{dx}\right] \\ $$

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