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Question Number 223187 Answers: 2 Comments: 0

Question Number 223191 Answers: 0 Comments: 0

Evaluate ; ∫_0 ^1 Π_(n=1) ^∞ (1−q^(4n) )^6 dq

$$ \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\mathrm{Evaluate}}\:;\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\left(\mathrm{1}−{q}^{\mathrm{4}{n}} \right)^{\mathrm{6}} \:{dq} \\ $$$$ \\ $$

Question Number 223179 Answers: 1 Comments: 1

If: xy = e^(𝛑/4) Find: tg (ln ((x^3 /y))) ∙ tg (ln ((y^3 /x))) = ?

$$\mathrm{If}:\:\:\:\mathrm{xy}\:=\:\boldsymbol{\mathrm{e}}^{\frac{\boldsymbol{\pi}}{\mathrm{4}}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{tg}\:\left(\mathrm{ln}\:\left(\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{y}}\right)\right)\:\centerdot\:\mathrm{tg}\:\left(\mathrm{ln}\:\left(\frac{\mathrm{y}^{\mathrm{3}} }{\mathrm{x}}\right)\right)\:=\:? \\ $$

Question Number 223169 Answers: 0 Comments: 0

evaluate Σ_(h=1) ^∞ (((−1)^(h−1) )/p_h ) , p_h ∈P(Set of primes) , h∈Z

$$\mathrm{evaluate}\: \\ $$$$\underset{{h}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{h}−\mathrm{1}} }{{p}_{{h}} }\:\:,\:{p}_{{h}} \in\mathbb{P}\left(\mathrm{Set}\:\mathrm{of}\:\mathrm{primes}\right)\:,\:{h}\in\mathbb{Z} \\ $$

Question Number 223161 Answers: 2 Comments: 4

Solve for x if (√(x+1))+(√(x−1))=1

$${Solve}\:{for}\:{x}\:{if} \\ $$$$\:\sqrt{{x}+\mathrm{1}}+\sqrt{{x}−\mathrm{1}}=\mathrm{1} \\ $$

Question Number 223157 Answers: 2 Comments: 0

Question Number 223139 Answers: 2 Comments: 1

Question Number 223137 Answers: 1 Comments: 1

Question Number 223123 Answers: 0 Comments: 0

∫_0 ^1 ln(cos(1−x+x^2 )∙sec(x^2 ) dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\mathrm{ln}\left(\mathrm{cos}\left(\mathrm{1}−{x}+{x}^{\mathrm{2}} \right)\centerdot\mathrm{sec}\left({x}^{\mathrm{2}} \right)\:\mathrm{d}{x}\right. \\ $$$$ \\ $$

Question Number 223116 Answers: 1 Comments: 1

∫_0 ^( 1) ln^5 (x^2 +1) dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{ln}^{\mathrm{5}} \left({x}^{\mathrm{2}} \:+\mathrm{1}\right)\:{dx} \\ $$$$ \\ $$

Question Number 223112 Answers: 0 Comments: 2

Question Number 223110 Answers: 1 Comments: 0

Question Number 223101 Answers: 0 Comments: 6

Question Number 223096 Answers: 1 Comments: 0

∫_(−(1/( (√3)))) ^(1/( (√3))) (x^4 /(1−x^4 ))cos^(−1) ((2/(1+x^2 )))dx=?

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

Question Number 223085 Answers: 1 Comments: 0

Question Number 223082 Answers: 0 Comments: 0

if lim_(x→+∞) x−f(x)=+∞ and lim_(x→+∞) x+f(x)=+∞ can we determine lim_(x→+∞) ((x−f(x))/(x+f(x)))

$${if}\:\underset{{x}\rightarrow+\infty} {{lim}x}−{f}\left({x}\right)=+\infty\:{and}\:\underset{{x}\rightarrow+\infty} {{lim}x}+{f}\left({x}\right)=+\infty \\ $$$${can}\:{we}\:{determine}\:\underset{{x}\rightarrow+\infty} {{lim}}\frac{{x}−{f}\left({x}\right)}{{x}+{f}\left({x}\right)} \\ $$$$ \\ $$

Question Number 223078 Answers: 1 Comments: 0

Evaluate : ∫ ((ln x ln(1+x^2 ))/x) dx

$$ \\ $$$$\:\:\:\:\:\:\mathrm{Evaluate}\::\:\int\:\frac{\mathrm{ln}\:{x}\:\mathrm{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{{x}}\:\mathrm{d}{x}\: \\ $$$$ \\ $$

Question Number 223076 Answers: 0 Comments: 0

Evaluate : ∫_0 ^1 ln^3 (1−x) ln^2 (x+1) dx

$$ \\ $$$$\:\:\:\:\:\:\:\mathrm{Evaluate}\::\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{ln}^{\mathrm{3}} \left(\mathrm{1}−{x}\right)\:\mathrm{ln}^{\mathrm{2}} \left({x}+\mathrm{1}\right)\:\mathrm{d}{x}\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 223079 Answers: 1 Comments: 0

Evaluate : ∫_0 ^1 ((arctan(x))/x) Li_2 (x) dx

$$\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\boldsymbol{\mathrm{Evaluate}}\::\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{arctan}\left({x}\right)}{{x}}\:\mathrm{Li}_{\mathrm{2}} \left({x}\right)\:\mathrm{d}{x} \\ $$$$ \\ $$

Question Number 223125 Answers: 1 Comments: 0

Question Number 223124 Answers: 3 Comments: 0

Question Number 223066 Answers: 1 Comments: 1

Question Number 223055 Answers: 1 Comments: 2

Question Number 223054 Answers: 0 Comments: 0

find y y^dy = x^dx

$$\mathrm{find}\:{y} \\ $$$${y}^{{dy}} =\:{x}^{{dx}} \\ $$

Question Number 223090 Answers: 1 Comments: 1

∫_0 ^∞ (x^2 /((cosh(x^2 ))^2 ))dx

$$\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{2}} }{\left(\mathrm{cosh}\left({x}^{\mathrm{2}} \right)\right)^{\mathrm{2}} }\mathrm{d}{x} \\ $$

Question Number 223044 Answers: 0 Comments: 1

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