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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

Question Number 223042 Answers: 1 Comments: 12

Question Number 223040 Answers: 0 Comments: 1

Question Number 223032 Answers: 1 Comments: 0

Π_(t=0) ^2^(2024) (4sin^2 ((tπ)/2^(2025) )−3)

$$ \\ $$$$\:\:\:\:\underset{{t}=\mathrm{0}} {\overset{\mathrm{2}^{\mathrm{2024}} } {\prod}}\left(\mathrm{4sin}^{\mathrm{2}} \frac{{t}\pi}{\mathrm{2}^{\mathrm{2025}} }−\mathrm{3}\right) \\ $$

Question Number 223025 Answers: 0 Comments: 0

Question Number 223007 Answers: 0 Comments: 6

everyone or Mr. Gaster ! Please help me how to sove the integral Because the integral is very crazy or very Complicated Problem; ∫_0 ^( 1) ln(x−1) ln(x+1) ln (x^2 + 1) tan^(−1) (x) dx =???

$$ \\ $$$$\:\:\:\:\:\:\mathrm{everyone}\:\mathrm{or}\:\mathrm{Mr}.\:\mathrm{Gaster}\:! \\ $$$$\:\:\:\:\:\:\:\mathrm{Please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{how}\:\mathrm{to}\:\mathrm{sove}\:\mathrm{the}\:\mathrm{integral}\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{Because}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{is}\:\mathrm{very}\:\mathrm{crazy}\:\mathrm{or}\:\mathrm{very}\:\mathrm{Complicated} \\ $$$$\:\:\:\:\:\:\mathrm{Problem}; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{ln}\left({x}−\mathrm{1}\right)\:\mathrm{ln}\left({x}+\mathrm{1}\right)\:\mathrm{ln}\:\left({x}^{\mathrm{2}} \:+\:\mathrm{1}\right)\:\mathrm{tan}^{−\mathrm{1}} \left({x}\right)\:\mathrm{d}{x}\:=??? \\ $$$$ \\ $$

Question Number 223006 Answers: 1 Comments: 0

L { tsin((√t) )}=?

$$ \\ $$$$\:\:\:\:\:\:\:\:\mathscr{L}\:\:\left\{\:{tsin}\left(\sqrt{{t}}\:\right)\right\}=? \\ $$

Question Number 223000 Answers: 1 Comments: 1

Π_(n=1) ^∞ ((1/e)(((n+1)/n))^n )^((−1)^n ) =((e∙(√π)∙(2)^(1/6) )/A^6 )

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\frac{\mathrm{1}}{{e}}\left(\frac{{n}+\mathrm{1}}{{n}}\right)^{{n}} \right)^{\left(−\mathrm{1}\right)^{{n}} } =\frac{{e}\centerdot\sqrt{\pi}\centerdot\sqrt[{\mathrm{6}}]{\mathrm{2}}}{{A}^{\mathrm{6}} } \\ $$

Question Number 222996 Answers: 2 Comments: 0

∫_0 ^1 (2−x^2 )^(3/2) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{2}−{x}^{\mathrm{2}} \right)^{\mathrm{3}/\mathrm{2}} {dx} \\ $$

Question Number 222995 Answers: 1 Comments: 0

Question Number 222993 Answers: 0 Comments: 1

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