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Question Number 91631 Answers: 0 Comments: 1

find a equivalent of Σ_(k=2) ^n ln(k)

$${find}\:{a}\:{equivalent}\:{of}\:\sum_{{k}=\mathrm{2}} ^{{n}} {ln}\left({k}\right) \\ $$

Question Number 91630 Answers: 0 Comments: 1

show that ∫_(−(π/4)) ^(π/4) ((sin2x)/((2+cos2x)^2 ))ln(1+e^x )dx =(π/(16))−((π(√3))/(36))

$$\mathrm{show}\:\mathrm{that}\: \\ $$$$\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{sin2x}}{\left(\mathrm{2}+\mathrm{cos2x}\right)^{\mathrm{2}} }\mathrm{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{x}} \right)\mathrm{dx} \\ $$$$=\frac{\pi}{\mathrm{16}}−\frac{\pi\sqrt{\mathrm{3}}}{\mathrm{36}} \\ $$

Question Number 91624 Answers: 0 Comments: 4

Question Number 91622 Answers: 2 Comments: 1

((d(x!))/dx)=

$$\frac{\mathrm{d}\left(\mathrm{x}!\right)}{\mathrm{dx}}= \\ $$

Question Number 91621 Answers: 0 Comments: 1

calculate ∫_0 ^∞ sin(x^6 )dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:{sin}\left({x}^{\mathrm{6}} \right){dx} \\ $$

Question Number 91620 Answers: 0 Comments: 1

let f(x) =2 x−(√(x−1)) find ∫ ((f(x))/(f^(−1) (x)))dx and ∫ ln(((f(x))/(f^(−1) (x))))dx

$${let}\:{f}\left({x}\right)\:=\mathrm{2}\:{x}−\sqrt{{x}−\mathrm{1}} \\ $$$${find}\:\int\:\:\frac{{f}\left({x}\right)}{{f}^{−\mathrm{1}} \left({x}\right)}{dx}\:\:{and}\:\:\int\:{ln}\left(\frac{{f}\left({x}\right)}{{f}^{−\mathrm{1}} \left({x}\right)}\right){dx} \\ $$

Question Number 91619 Answers: 0 Comments: 1

calculate ∫_2 ^(+∞) (((−1)^([2x]) )/(x[x]−1))dx

$${calculate}\:\int_{\mathrm{2}} ^{+\infty} \:\frac{\left(−\mathrm{1}\right)^{\left[\mathrm{2}{x}\right]} }{{x}\left[{x}\right]−\mathrm{1}}{dx} \\ $$

Question Number 91615 Answers: 0 Comments: 2

hi every one is it right if we use tylor in this integration and if there were another way that will be very cool ∫sin(x^4 )dx

$${hi}\:{every}\:{one}\:{is}\:{it}\:{right}\:{if}\:{we}\:{use}\:{tylor} \\ $$$${in}\:{this}\:{integration}\:{and}\:{if}\:{there}\:{were} \\ $$$${another}\:{way}\:{that}\:{will}\:{be}\:{very}\:{cool} \\ $$$$\int{sin}\left({x}^{\mathrm{4}} \right){dx}\: \\ $$$$ \\ $$$$ \\ $$

Question Number 91613 Answers: 1 Comments: 4

solve without using l′hopital lim_(x→e) ((ln(x)−1)/((e/x)−1))

$${solve}\:{without}\:{using}\:{l}'{hopital} \\ $$$$\underset{{x}\rightarrow{e}} {{lim}}\frac{{ln}\left({x}\right)−\mathrm{1}}{\frac{{e}}{{x}}−\mathrm{1}} \\ $$

Question Number 91611 Answers: 0 Comments: 1

find the volume of the region between curves (xy=4 and x+y=5) revolvex around the X axis

$$\:{find}\:{the}\:{volume}\:{of}\:{the}\:{region}\: \\ $$$${between}\:{curves}\:\left({xy}=\mathrm{4}\:{and}\:{x}+{y}=\mathrm{5}\right) \\ $$$${revolvex}\:{around}\:{the}\:{X}\:{axis} \\ $$

Question Number 91608 Answers: 0 Comments: 2

Question Number 91604 Answers: 0 Comments: 0

Question Number 91603 Answers: 0 Comments: 1

calculate ∫_0 ^∞ xe^(−x^2 −[x]) dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} {xe}^{−{x}^{\mathrm{2}} −\left[{x}\right]} \:{dx} \\ $$

Question Number 91599 Answers: 0 Comments: 1

Question Number 91595 Answers: 1 Comments: 2

what′s meaning of (x^. ) or (x^(..) )? are (x^. )=x′?

$$\mathrm{what}'\mathrm{s}\:\mathrm{meaning}\:\mathrm{of}\:\left(\overset{.} {\mathrm{x}}\right)\:\mathrm{or}\:\left(\overset{..} {\mathrm{x}}\right)? \\ $$$$\mathrm{are}\:\left(\overset{.} {\mathrm{x}}\right)=\mathrm{x}'? \\ $$

Question Number 91593 Answers: 1 Comments: 0

∫ ((sec x csc x dx)/(ln(tan^2 x))) ?

$$\int\:\frac{\mathrm{sec}\:{x}\:{csc}\:{x}\:{dx}}{\mathrm{ln}\left(\mathrm{tan}\:^{\mathrm{2}} {x}\right)}\:? \\ $$

Question Number 91588 Answers: 0 Comments: 2

what is f^(−1) for f(x)=⌊x⌋??

$${what}\:{is}\:{f}^{−\mathrm{1}} \:{for}\:{f}\left({x}\right)=\lfloor{x}\rfloor?? \\ $$

Question Number 91578 Answers: 0 Comments: 2

f((1/x))+2f(x)= ((4x^3 +6x)/(3x^2 )) f(x)=?

$$ \\ $$$${f}\left(\frac{\mathrm{1}}{{x}}\right)+\mathrm{2}{f}\left({x}\right)=\:\frac{\mathrm{4}{x}^{\mathrm{3}} +\mathrm{6}{x}}{\mathrm{3}{x}^{\mathrm{2}} } \\ $$$${f}\left({x}\right)=? \\ $$

Question Number 91568 Answers: 2 Comments: 0

Question Number 91560 Answers: 0 Comments: 2

x=((1+(√(2004)))/2) 4x^3 −2007x−2000=?

$${x}=\frac{\mathrm{1}+\sqrt{\mathrm{2004}}}{\mathrm{2}} \\ $$$$\mathrm{4}{x}^{\mathrm{3}} −\mathrm{2007}{x}−\mathrm{2000}=? \\ $$

Question Number 91558 Answers: 2 Comments: 1

(x^2 +1)y′+y^2 +1 = 0

$$\left({x}^{\mathrm{2}} +\mathrm{1}\right){y}'+{y}^{\mathrm{2}} +\mathrm{1}\:=\:\mathrm{0}\: \\ $$

Question Number 91555 Answers: 1 Comments: 4

Question Number 91542 Answers: 2 Comments: 3

∫ (x^3 /(2x+1)) dx = ?

$$\int\:\frac{{x}^{\mathrm{3}} }{\mathrm{2}{x}+\mathrm{1}}\:{dx}\:=\:? \\ $$

Question Number 91534 Answers: 0 Comments: 3

∫_1 ^∞ ((sin^2 (x))/x^2 )dx

$$\int_{\mathrm{1}} ^{\infty} \frac{{sin}^{\mathrm{2}} \left({x}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 91521 Answers: 0 Comments: 8

given that the composite function f^2 (x) = 64x+45 find f(x)

$${given}\:{that}\:{the}\: \\ $$$${composite} \\ $$$${function}\:{f}^{\mathrm{2}} \left({x}\right)\:=\:\mathrm{64}{x}+\mathrm{45}\: \\ $$$${find}\:{f}\left({x}\right)\: \\ $$

Question Number 91509 Answers: 0 Comments: 2

does anyone know Glauss′ law for magnetism? tanks

$${does}\:{anyone}\:{know}\:{Glauss}'\:{law}\:{for}\:{magnetism}?\:{tanks} \\ $$

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