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Question Number 222411 Answers: 3 Comments: 0

[ 1 .] ∫_0 ^( 1) ((ln(x) ln(1−x^2 )ln(1+x^2 ))/(1−x^2 )) dx [ 2 .] ∫_0 ^1 ((ln(x) ln(1−x) ln(1+x) ln(1+x^2 ))/(1+x)) dx [ 3 .] ∫_0 ^1 ((ln(x) ln(1−x^2 ) ln(1+x^2 ))/x) dx [ 4 .] ∫_0 ^( 1) ((ln(x) ln(1−x) ln(1+x) ln(1−x^2 ))/x) dx

Question Number 222568 Answers: 0 Comments: 0

f(x)=((√(x−2)))^0 and g(x)=(√((x−2)^0 )) dom f(x)=? , dom g(x)=?

$${f}\left({x}\right)=\left(\sqrt{{x}−\mathrm{2}}\right)^{\mathrm{0}} \:\:{and}\:{g}\left({x}\right)=\sqrt{\left({x}−\mathrm{2}\right)^{\mathrm{0}} } \\ $$$${dom}\:{f}\left({x}\right)=?\:,\:{dom}\:{g}\left({x}\right)=? \\ $$

Question Number 222436 Answers: 1 Comments: 0

Question Number 222409 Answers: 0 Comments: 0

Solve ; ∫_0 ^(π/2) ((ln^n sin θ)/(sin^p θ cos^q θ)) dθ , for n,p,q ∈ R_(≥ 0)

$$ \\ $$$$\:\:\:\mathrm{Solve}\:;\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{ln}^{{n}} \:\mathrm{sin}\:\theta}{\mathrm{sin}^{{p}} \:\theta\:\mathrm{cos}^{{q}} \:\theta}\:\mathrm{d}\theta\:,\:\mathrm{for}\:{n},{p},{q}\:\in\:\mathbb{R}_{\geqslant\:\mathrm{0}} \:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 222404 Answers: 1 Comments: 0

Question Number 222408 Answers: 1 Comments: 0

∫_1 ^∞ ((1/x))^(x/( (√(x−1)))) dx = ??

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{1}} ^{\infty} \:\left(\frac{\mathrm{1}}{{x}}\right)^{\frac{{x}}{\:\sqrt{{x}−\mathrm{1}}}} \:{dx}\:=\:\:\:?? \\ $$$$ \\ $$

Question Number 222389 Answers: 0 Comments: 0

Prove: ∫_0 ^∞ ((cos(nx)cos(p arctan x))/((1+x^2 )^(p/2) ))=(π/2) ((n^(p−1) e^(−n) )/(Γ(p))) (p>0)

$$\mathrm{Prove}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{cos}\left({nx}\right)\mathrm{cos}\left({p}\:\mathrm{arctan}\:{x}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\frac{{p}}{\mathrm{2}}} }=\frac{\pi}{\mathrm{2}}\:\frac{{n}^{{p}−\mathrm{1}} {e}^{−{n}} }{\Gamma\left({p}\right)}\:\left({p}>\mathrm{0}\right) \\ $$

Question Number 222385 Answers: 1 Comments: 2

Question Number 222376 Answers: 1 Comments: 0

Question Number 222373 Answers: 2 Comments: 0

An 80 kg man floats with 4% of his volume above the surface in fresh water.what is his volume? what volume would be above the surface in Sea water?How great is the upthrust on him in air due to the air he displaces? density of sea water =1030kgm^-3, density of fresh water=1000kgm^-3?

Question Number 222356 Answers: 1 Comments: 0

∫_0 ^( ∞) f(r)dr=1 , ∫_0 ^( ∞) g(r)dr=1 ∫_(−∞i+𝛄) ^( ∞i+𝛄) F(t)G(t)dt=?? F(t)=∫_0 ^( ∞) f(r)e^(−rt) dr , G(t)=∫_0 ^( ∞) g(r)e^(−rt) dr

$$\int_{\mathrm{0}} ^{\:\infty} \:{f}\left({r}\right)\mathrm{d}{r}=\mathrm{1}\:,\:\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{g}\left({r}\right)\mathrm{d}{r}=\mathrm{1} \\ $$$$\int_{−\infty\boldsymbol{{i}}+\boldsymbol{\gamma}} ^{\:\:\infty\boldsymbol{{i}}+\boldsymbol{\gamma}} \:{F}\left({t}\right){G}\left({t}\right)\mathrm{d}{t}=?? \\ $$$${F}\left({t}\right)=\int_{\mathrm{0}} ^{\:\infty} \:{f}\left({r}\right){e}^{−{rt}} \mathrm{d}{r}\:,\:{G}\left({t}\right)=\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{g}\left({r}\right){e}^{−{rt}} \mathrm{d}{r} \\ $$

Question Number 222353 Answers: 1 Comments: 1

solve; ((11)/(29)) = ? , no fraction and no decimal

$$ \\ $$$$\:\:\:\:\:\mathrm{solve};\:\:\frac{\mathrm{11}}{\mathrm{29}}\:=\:?\:,\:\mathrm{no}\:\mathrm{fraction}\:\mathrm{and}\:\mathrm{no}\:\mathrm{decimal}\:\:\:\:\: \\ $$$$ \\ $$

Question Number 222352 Answers: 1 Comments: 0

Prove that : (a−b)(a−c)(a−d)(b−c)(b−d)(c−d) divisible by 12, with a,b,c,d ∈Z

$${Prove}\:{that}\::\:\left({a}−{b}\right)\left({a}−{c}\right)\left({a}−{d}\right)\left({b}−{c}\right)\left({b}−{d}\right)\left({c}−{d}\right)\:{divisible}\:{by}\:\mathrm{12},\:{with}\:{a},{b},{c},{d}\:\in\mathbb{Z} \\ $$

Question Number 222339 Answers: 2 Comments: 0

Solve: ((36))^(1/x) + ((24))^(1/x) = ((16))^(1/x)

$$\mathrm{Solve}:\:\:\:\:\:\:\sqrt[{\mathrm{x}}]{\mathrm{36}}\:\:\:+\:\:\:\sqrt[{\mathrm{x}}]{\mathrm{24}}\:\:\:\:=\:\:\:\sqrt[{\mathrm{x}}]{\mathrm{16}} \\ $$

Question Number 222336 Answers: 0 Comments: 0

∫∫∫ ((−y ± (√(y^2 + 4xy)))/(2x)) dxdydz

$$ \\ $$$$\:\:\:\:\:\:\:\int\int\int\:\:\frac{−{y}\:\pm\:\sqrt{{y}^{\mathrm{2}} \:+\:\mathrm{4}{xy}}}{\mathrm{2}{x}}\:{dxdydz} \\ $$$$ \\ $$

Question Number 222334 Answers: 1 Comments: 4

Question Number 222331 Answers: 0 Comments: 0

Find closed form; ∫_( 0) ^( 1) ((Li_2 (z^2 )Li_2 (−z^2 ))/(1 + z^2 )) dz = ?

$$ \\ $$$$\:\:\:\:\:\:\:\mathrm{Find}\:\mathrm{closed}\:\mathrm{form}; \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{Li}_{\mathrm{2}} \left({z}^{\mathrm{2}} \right)\mathrm{Li}_{\mathrm{2}} \left(−{z}^{\mathrm{2}} \right)}{\mathrm{1}\:+\:{z}^{\mathrm{2}} }\:\mathrm{d}{z}\:=\:? \\ $$

Question Number 222329 Answers: 0 Comments: 1

lim_(x→∞) 4x+(√(16x^2 −3x))

$$\boldsymbol{\mathrm{lim}}_{\boldsymbol{\mathrm{x}}\rightarrow\infty} \:\mathrm{4}\boldsymbol{\mathrm{x}}+\sqrt{\mathrm{16}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{3}\boldsymbol{\mathrm{x}}} \\ $$$$ \\ $$

Question Number 222323 Answers: 1 Comments: 0

a+3^b =b,3^b ∙a^(b+1) max=?

$${a}+\mathrm{3}^{{b}} ={b},\mathrm{3}^{{b}} \centerdot{a}^{{b}+\mathrm{1}} \:\mathrm{max}=? \\ $$

Question Number 222317 Answers: 1 Comments: 0

∫_0 ^( ∞) f(z)dz=(π/2) , ∫_0 ^( ∞) g(z)dz=1 (2/π)∫_0 ^( ∞) f(z)g(z)dz=??

$$\int_{\mathrm{0}} ^{\:\infty} \:{f}\left({z}\right)\mathrm{d}{z}=\frac{\pi}{\mathrm{2}}\:,\:\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{g}\left({z}\right)\mathrm{d}{z}=\mathrm{1} \\ $$$$\frac{\mathrm{2}}{\pi}\int_{\mathrm{0}} ^{\:\infty} \:{f}\left({z}\right)\mathrm{g}\left({z}\right)\mathrm{d}{z}=?? \\ $$

Question Number 222312 Answers: 1 Comments: 0

Question Number 222309 Answers: 2 Comments: 0

determinant (((4^x +6^x =9^x )))

$$\begin{array}{|c|}{\mathrm{4}^{{x}} +\mathrm{6}^{{x}} =\mathrm{9}^{{x}} }\\\hline\end{array} \\ $$

Question Number 222300 Answers: 0 Comments: 5

How do you put a box around something?? please tell me

$${How}\:{do}\:{you}\:{put}\:{a}\:{box}\:{around}\:{something}??\:{please}\:{tell}\:{me} \\ $$

Question Number 222299 Answers: 1 Comments: 0

For what value of k the roots of the equation ((x^2 −2x)/(4x−1))=((k−1)/(k+1)) will have same value but with opposite symbol(like x=a and −a) i mean the two valuea of x will be this type x=2 and −2(both 2 but opposite symbols)

$${For}\:{what}\:{value}\:{of}\:\:{k}\:\:{the}\:{roots}\:{of}\:{the}\:{equation} \\ $$$$\frac{{x}^{\mathrm{2}} −\mathrm{2}{x}}{\mathrm{4}{x}−\mathrm{1}}=\frac{{k}−\mathrm{1}}{{k}+\mathrm{1}} \\ $$$${will}\:{have}\:{same}\:{value}\:{but}\:\:{with}\:{opposite}\:{symbol}\left({like}\:{x}={a}\:{and}\:−{a}\right) \\ $$$${i}\:{mean}\:{the}\:{two}\:{valuea}\:{of}\:{x}\:{will}\:{be}\:{this}\:{type} \\ $$$${x}=\mathrm{2}\:{and}\:−\mathrm{2}\left({both}\:\mathrm{2}\:{but}\:{opposite}\:{symbols}\right) \\ $$

Question Number 222295 Answers: 1 Comments: 0

Question Number 222292 Answers: 1 Comments: 0

∫_(−∞) ^∞ sech(z) sech(z−a) dz

$$ \\ $$$$\:\:\:\int_{−\infty} ^{\infty} \mathrm{sech}\left({z}\right)\:\mathrm{sech}\left({z}−{a}\right)\:{dz} \\ $$$$ \\ $$

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