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Question Number 96479 Answers: 1 Comments: 0

show that ∫_1 ^e ((x−xln(x)+1)/(x(x+1)^2 +x ln^2 (x)))dx=arctan((1/(e+1)))

$${show}\:{that} \\ $$$$\int_{\mathrm{1}} ^{{e}} \frac{{x}−{xln}\left({x}\right)+\mathrm{1}}{{x}\left({x}+\mathrm{1}\right)^{\mathrm{2}} +{x}\:{ln}^{\mathrm{2}} \left({x}\right)}{dx}={arctan}\left(\frac{\mathrm{1}}{{e}+\mathrm{1}}\right) \\ $$

Question Number 96467 Answers: 1 Comments: 0

Suppose y = 8 ; (dy/dx) = 4 & (d^2 y/dx^2 ) ∣_(x=1) = −2 . Find the value of (1) ((d(xy))/dx) ∣_(x=1) (1)((d^2 (xy))/dx^2 ) ∣_(x=1)

$$\mathrm{Suppose}\:\mathrm{y}\:=\:\mathrm{8}\:;\:\frac{{dy}}{{dx}}\:=\:\mathrm{4}\:\&\: \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:\mid_{{x}=\mathrm{1}} \:=\:−\mathrm{2}\:.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\left(\mathrm{1}\right)\:\frac{{d}\left({xy}\right)}{{dx}}\:\mid_{{x}=\mathrm{1}} \\ $$$$\left(\mathrm{1}\right)\frac{{d}^{\mathrm{2}} \left({xy}\right)}{{dx}^{\mathrm{2}} }\:\mid_{{x}=\mathrm{1}} \: \\ $$$$ \\ $$

Question Number 96466 Answers: 0 Comments: 0

Question Number 96460 Answers: 1 Comments: 8

Question Number 96454 Answers: 1 Comments: 0

Question Number 96441 Answers: 1 Comments: 1

Question Number 96437 Answers: 1 Comments: 0

Question Number 96436 Answers: 0 Comments: 0

∮ x^2 dx = ???

$$\oint\:{x}^{\mathrm{2}} \:{dx}\:=\:??? \\ $$

Question Number 96429 Answers: 1 Comments: 0

Question Number 96428 Answers: 2 Comments: 0

Question Number 96427 Answers: 0 Comments: 0

Question Number 96419 Answers: 5 Comments: 3

Question Number 96410 Answers: 0 Comments: 4

Question Number 96407 Answers: 1 Comments: 4

Question Number 96397 Answers: 1 Comments: 0

Hello If 5000F is the price to carry 5 tonnes of water on 5 kilometers, what is the price to carry 60 tonnes on 70.5 kilometers? please explain if possible...

$${Hello} \\ $$$${If}\:\:\mathrm{5000}{F}\:{is}\:{the}\:{price}\:{to}\:{carry}\:\mathrm{5}\:{tonnes} \\ $$$${of}\:{water}\:{on}\:\mathrm{5}\:{kilometers},\:{what}\:{is}\:{the} \\ $$$${price}\:{to}\:{carry}\:\mathrm{60}\:{tonnes}\:{on}\:\mathrm{70}.\mathrm{5}\: \\ $$$${kilometers}? \\ $$$${please}\:{explain}\:{if}\:{possible}... \\ $$

Question Number 96394 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((ln(1+x).ln(1+(1/x^2 )))/x)dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right).\mathrm{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\right)}{\mathrm{x}}\mathrm{dx} \\ $$

Question Number 96392 Answers: 1 Comments: 0

solve (dy/dx) = (4x+y+1)^2 , when y(0) = 1

$$\mathrm{solve}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\left(\mathrm{4x}+\mathrm{y}+\mathrm{1}\right)^{\mathrm{2}} \:,\:\mathrm{when}\: \\ $$$$\mathrm{y}\left(\mathrm{0}\right)\:=\:\mathrm{1} \\ $$

Question Number 96383 Answers: 1 Comments: 0

Find domain & range of function f(x) = (1/(x^2 −5x+6))

$$\mathrm{Find}\:\mathrm{domain}\:\&\:\mathrm{range}\:\mathrm{of}\:\mathrm{function}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{6}}\: \\ $$

Question Number 96377 Answers: 1 Comments: 0

if tan(x+iy)=a+ib determine x and y interms of a and b

$$\mathrm{if}\:\mathrm{tan}\left(\mathrm{x}+\mathrm{iy}\right)=\mathrm{a}+\mathrm{ib}\:\:\:\mathrm{determine}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{interms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b} \\ $$

Question Number 96375 Answers: 2 Comments: 0

let P(x) =(1+x^2 )(1+x^4 )...(1+x^2^n ) 1) solve inside C the equation P(x)=0 2) factorize P(x) inside C[x] 3) calvulate P^′ (x) 4) decompose F =(1/(P(x)))

$$\mathrm{let}\:\mathrm{P}\left(\mathrm{x}\right)\:=\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{1}+\mathrm{x}^{\mathrm{4}} \right)...\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}^{\mathrm{n}} } \right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{solve}\:\mathrm{inside}\:\mathrm{C}\:\:\mathrm{the}\:\mathrm{equation}\:\mathrm{P}\left(\mathrm{x}\right)=\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{factorize}\:\mathrm{P}\left(\mathrm{x}\right)\:\mathrm{inside}\:\mathrm{C}\left[\mathrm{x}\right] \\ $$$$\left.\mathrm{3}\right)\:\mathrm{calvulate}\:\mathrm{P}^{'} \left(\mathrm{x}\right) \\ $$$$\left.\mathrm{4}\right)\:\mathrm{decompose}\:\mathrm{F}\:=\frac{\mathrm{1}}{\mathrm{P}\left(\mathrm{x}\right)} \\ $$

Question Number 96373 Answers: 2 Comments: 0

1. find ∫_1 ^(+∞) (dx/(x^2 −i)) and ∫_1 ^(+∞) (dx/(x^2 +i)) (i=(√(−1))) 2. find the value of ∫_1 ^(+∞) (dx/(x^4 +1))

$$\mathrm{1}.\:\mathrm{find}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} −\mathrm{i}}\:\:\mathrm{and}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{i}}\:\:\:\:\left(\mathrm{i}=\sqrt{−\mathrm{1}}\right) \\ $$$$\mathrm{2}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\int_{\mathrm{1}} ^{+\infty} \:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{4}} \:+\mathrm{1}} \\ $$

Question Number 96365 Answers: 2 Comments: 0

Question Number 96358 Answers: 0 Comments: 0

Question Number 96350 Answers: 1 Comments: 2

Question Number 96349 Answers: 0 Comments: 1

Question Number 96390 Answers: 1 Comments: 0

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