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Question Number 72015    Answers: 0   Comments: 1

find ∫ ((arctan(x−(1/x)))/(x^2 +1))dx

$${find}\:\int\:\:\frac{{arctan}\left({x}−\frac{\mathrm{1}}{{x}}\right)}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx} \\ $$

Question Number 72012    Answers: 0   Comments: 1

find f(α) =∫_0 ^∞ ((arctan(αx))/((x^2 +3)^2 ))dx with α real.

$${find}\:{f}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\alpha{x}\right)}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} }{dx}\:\:{with}\:\alpha\:{real}. \\ $$

Question Number 72011    Answers: 1   Comments: 1

calculate ∫_0 ^∞ ((ln(3+x^2 ))/((x^2 +1)^2 ))dx

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

Question Number 71993    Answers: 1   Comments: 0

Question Number 71986    Answers: 1   Comments: 0

Question Number 71984    Answers: 1   Comments: 0

x, y ∈ I ⊂ R prove that ∣cosx − siny∣ ≤ ∣x − y∣

$$\:{x},\:{y}\:\in\:{I}\:\subset\:\mathbb{R}\:\:{prove}\:\:{that}\:\:\mid{cosx}\:−\:{siny}\mid\:\leqslant\:\mid{x}\:−\:{y}\mid \\ $$

Question Number 71983    Answers: 1   Comments: 0

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Question Number 74587    Answers: 0   Comments: 0

If sum of n arithmetic means between two number is 20.if last mean is double of 1st mean and one is three times of another number. find the numbers.

$$\mathrm{If}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{n}\:\mathrm{arithmetic}\:\mathrm{means}\:\mathrm{between}\: \\ $$$$\mathrm{two}\:\mathrm{number}\:\mathrm{is}\:\mathrm{20}.\mathrm{if}\:\mathrm{last}\:\mathrm{mean}\:\mathrm{is}\:\mathrm{double} \\ $$$$\mathrm{of}\:\mathrm{1st}\:\mathrm{mean}\:\mathrm{and}\:\mathrm{one}\:\mathrm{is}\:\mathrm{three}\:\mathrm{times}\:\mathrm{of} \\ $$$$\mathrm{another}\:\mathrm{number}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{numbers}. \\ $$$$ \\ $$

Question Number 71972    Answers: 0   Comments: 2

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Question Number 71964    Answers: 5   Comments: 1

Question Number 71960    Answers: 1   Comments: 0

Question Number 71957    Answers: 0   Comments: 0

Question Number 71955    Answers: 1   Comments: 1

Question Number 71946    Answers: 1   Comments: 0

Question Number 71939    Answers: 1   Comments: 1

Question Number 71944    Answers: 1   Comments: 0

Question Number 71925    Answers: 1   Comments: 0

Solve (√(1 − x^2 )) = x^(4/3)

$$\:\boldsymbol{{Solve}}\:\:\sqrt{\mathrm{1}\:−\:\boldsymbol{{x}}^{\mathrm{2}} }\:=\:\boldsymbol{{x}}^{\mathrm{4}/\mathrm{3}} \\ $$

Question Number 71921    Answers: 0   Comments: 0

Question Number 72062    Answers: 1   Comments: 2

Question Number 71904    Answers: 0   Comments: 0

Question Number 71903    Answers: 2   Comments: 0

ax + by = 3 ax^2 + by^2 = 7 ax^3 + by^3 = 16 ax^4 + by^4 = 42 ax^5 + by^5 = ?

$${ax}\:+\:{by}\:\:=\:\:\mathrm{3} \\ $$$${ax}^{\mathrm{2}} \:+\:{by}^{\mathrm{2}} \:\:=\:\:\mathrm{7} \\ $$$${ax}^{\mathrm{3}} \:+\:{by}^{\mathrm{3}} \:\:=\:\:\mathrm{16} \\ $$$${ax}^{\mathrm{4}} \:+\:{by}^{\mathrm{4}} \:\:=\:\:\mathrm{42} \\ $$$${ax}^{\mathrm{5}} \:+\:{by}^{\mathrm{5}} \:\:=\:\:? \\ $$$$ \\ $$

Question Number 71926    Answers: 1   Comments: 2

Question Number 71894    Answers: 0   Comments: 1

lim_(x→(π/2)) (sin x)^(tanx)

$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\left(\mathrm{sin}\:\mathrm{x}\right)^{\mathrm{tanx}} \\ $$

Question Number 71991    Answers: 1   Comments: 0

Question Number 71886    Answers: 0   Comments: 0

Question Number 71868    Answers: 0   Comments: 3

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