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Question Number 222529 Answers: 0 Comments: 0

∫_0 ^∞ x(x^2 +1)^(−x+(1/x) ) dx = ??

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \:{x}\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{−{x}+\frac{\mathrm{1}}{{x}}\:} \:{dx}\:=\:?? \\ $$$$ \\ $$

Question Number 222552 Answers: 1 Comments: 0

x^x =64 , x=?

$${x}^{{x}} =\mathrm{64}\:\:\:\:\:\:,\:\:{x}=? \\ $$

Question Number 222523 Answers: 1 Comments: 0

x+V−J(x)((ustx)/(zac^2 x))=x−((ustx_0 )/( (√x)ψ+ζ(((−1+v%)/(π+2))+L_(l(x→0)) ^( v%) X_(2x^2 ) ^( 1) )))

$${x}+{V}−{J}\left({x}\right)\frac{{ustx}}{{zac}^{\mathrm{2}} {x}}={x}−\frac{{ustx}_{\mathrm{0}} }{\:\sqrt{{x}}\psi+\zeta\left(\frac{−\mathrm{1}+{v\%}}{\pi+\mathrm{2}}+\mathscr{L}_{{l}\left({x}\rightarrow\mathrm{0}\right)} ^{\:\:{v\%}} {X}_{\mathrm{2}{x}^{\mathrm{2}} } ^{\:\mathrm{1}} \right)} \\ $$

Question Number 222521 Answers: 1 Comments: 1

−3ix+(π/2)+((ix−(√(5π)))/6)=0 x=?

$$−\mathrm{3}{ix}+\frac{\pi}{\mathrm{2}}+\frac{{ix}−\sqrt{\mathrm{5}\pi}}{\mathrm{6}}=\mathrm{0} \\ $$$${x}=?\: \\ $$

Question Number 222516 Answers: 2 Comments: 0

Given the integer k,how to find the incomplete general solution for the non-trivial integer solutions of the Diophantine equation: a^4 +b^4 +ka^2 b^2 =c^4 +d^4 +kc^2 d^2 ,a,b,c,d∈N,k∈Z,gcd(a,b,c,d)=1

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{integer}\:{k},\mathrm{how}\:\:\mathrm{to} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{incomplete}\:\mathrm{general} \\ $$$$\mathrm{solution}\:\mathrm{for}\:\mathrm{the}\:\mathrm{non}-\mathrm{trivial}\:\mathrm{integer} \\ $$$$\mathrm{solutions}\:\mathrm{of}\:\:\mathrm{the}\:\mathrm{Diophantine}\:\mathrm{equation}: \\ $$$${a}^{\mathrm{4}} +{b}^{\mathrm{4}} +{ka}^{\mathrm{2}} {b}^{\mathrm{2}} ={c}^{\mathrm{4}} +{d}^{\mathrm{4}} +{kc}^{\mathrm{2}} {d}^{\mathrm{2}} ,{a},{b},{c},{d}\in\mathbb{N},{k}\in\mathbb{Z},\mathrm{gcd}\left({a},{b},{c},{d}\right)=\mathrm{1} \\ $$

Question Number 222511 Answers: 0 Comments: 0

Is the statement correct? in const.“ x+a−bx^n ={0} ” x= { ((−a±((2b)/(n+1)) , n>0)),((N_b ^( a) ∫_b ^( a) G(n−1), n≤0)) :}

$${Is}\:{the}\:{statement}\:{correct}? \\ $$$${in}\:{const}.``\:{x}+{a}−{bx}^{{n}} =\left\{\mathrm{0}\right\}\:'' \\ $$$${x}=\begin{cases}{−{a}\pm\frac{\mathrm{2}{b}}{{n}+\mathrm{1}}\:,\:{n}>\mathrm{0}}\\{{N}_{{b}} ^{\:{a}} \:\int_{{b}} ^{\:{a}} {G}\left({n}−\mathrm{1}\right),\:{n}\leqslant\mathrm{0}}\end{cases} \\ $$

Question Number 222541 Answers: 0 Comments: 3

very very crazy problem, i am not found what is the result of this integral; ∫(1/( (√z) + (√(z−h)) + (√(z−2h)))) dz

$$ \\ $$$$\:\:\:\mathrm{very}\:\mathrm{very}\:\mathrm{crazy}\:\mathrm{problem},\:\:\mathrm{i}\:\mathrm{am}\:\mathrm{not}\:\mathrm{found} \\ $$$$\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{result}\:\mathrm{of}\:\mathrm{this}\:\mathrm{integral}; \\ $$$$\:\:\:\:\:\:\:\:\int\frac{\mathrm{1}}{\:\sqrt{{z}}\:+\:\sqrt{{z}−{h}}\:+\:\sqrt{{z}−\mathrm{2}{h}}}\:{dz} \\ $$$$ \\ $$

Question Number 222501 Answers: 1 Comments: 0

This is VERY HARD { ( { ((x+y=0)),((l(y)=1)) :}),( { ((x∈N)),((−y= { ((v%, for x↺γ(1))),((−v%, for x↬θ(∮_(−x) ^( 0) (c/7)))) :})) :}) :} x=?, y=?

$${This}\:{is}\:{VERY}\:{HARD} \\ $$$$\begin{cases}{\begin{cases}{{x}+{y}=\mathrm{0}}\\{{l}\left({y}\right)=\mathrm{1}}\end{cases}}\\{\begin{cases}{{x}\in\mathbb{N}}\\{−{y}=\begin{cases}{{v\%},\:\:{for}\:{x}\circlearrowleft\gamma\left(\mathrm{1}\right)}\\{−{v\%},\:\:{for}\:{x}\looparrowright\theta\left(\oint_{−{x}} ^{\:\mathrm{0}} \frac{{c}}{\mathrm{7}}\right)}\end{cases}}\end{cases}}\end{cases} \\ $$$${x}=?,\:{y}=? \\ $$

Question Number 222512 Answers: 1 Comments: 0

∫_0 ^(π/2) ((xsinxcosx)/(tan^2 x+cotan^2 x))dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{xsinxcosx}}{{tan}^{\mathrm{2}} {x}+{cotan}^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 222487 Answers: 0 Comments: 0

′Delete all lines′ function deletes all lines without asking after deleting all lines for the first time in the equation editor

$$'{Delete}\:{all}\:{lines}'\:{function}\:{deletes}\:{all}\:{lines}\:{without}\:{asking}\:{after}\:{deleting}\:{all}\:{lines}\:{for}\:{the}\:{first}\:{time}\:{in}\:{the}\:{equation}\:{editor} \\ $$

Question Number 222583 Answers: 0 Comments: 0

solve for p,q,s in terms of c. • (((qs)/(q−sp)))^2 −s(((qs)/(q−sp)))+p=0 • (((q+c)/(p+1)))^2 =sp−q • (q−cp)(p+1)^2 =(q+c)^3 I have to find non zero real x=−(((q+c)/(p+1))) .

$${solve}\:{for}\:{p},{q},{s}\:{in}\:{terms}\:{of}\:{c}. \\ $$$$\bullet\:\left(\frac{{qs}}{{q}−{sp}}\right)^{\mathrm{2}} −{s}\left(\frac{{qs}}{{q}−{sp}}\right)+{p}=\mathrm{0} \\ $$$$\bullet\:\left(\frac{{q}+{c}}{{p}+\mathrm{1}}\right)^{\mathrm{2}} ={sp}−{q} \\ $$$$\bullet\:\left({q}−{cp}\right)\left({p}+\mathrm{1}\right)^{\mathrm{2}} =\left({q}+{c}\right)^{\mathrm{3}} \\ $$$${I}\:{have}\:{to}\:{find}\:{non}\:{zero}\:{real}\:{x}=−\left(\frac{{q}+{c}}{{p}+\mathrm{1}}\right)\:. \\ $$

Question Number 222482 Answers: 2 Comments: 1