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Question Number 45173 Answers: 0 Comments: 3

Question Number 45232 Answers: 1 Comments: 1

calculate ∫_0 ^1 ln(x)ln(1+x)dx .

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

Question Number 45231 Answers: 2 Comments: 1

find ∫ (√((x−1)(3−x)))dx

$${find}\:\int\:\sqrt{\left({x}−\mathrm{1}\right)\left(\mathrm{3}−{x}\right)}{dx} \\ $$

Question Number 45225 Answers: 1 Comments: 0

solve for x 9^(x+1) +3^(2x+1) =36

$$\mathrm{solve}\:\mathrm{for}\:{x} \\ $$$$\mathrm{9}^{{x}+\mathrm{1}} +\mathrm{3}^{\mathrm{2}{x}+\mathrm{1}} =\mathrm{36} \\ $$

Question Number 45224 Answers: 1 Comments: 0

Question Number 45221 Answers: 1 Comments: 0

Find the divisors ; if any ; of 16000001

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{divisors}\:; \\ $$$$\mathrm{if}\:\mathrm{any}\:;\:\mathrm{of}\:\mathrm{16000001} \\ $$

Question Number 45155 Answers: 2 Comments: 1

Question Number 45151 Answers: 0 Comments: 2

Question Number 45166 Answers: 1 Comments: 0

Question Number 45165 Answers: 1 Comments: 0

Question Number 45164 Answers: 0 Comments: 6

Question Number 45163 Answers: 0 Comments: 0

Evaluate ∫_0 ^∞ ∫_0 ^t e^(−t) ((sinu)/u)du dt

$$\mathrm{Evaluate}\:\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\mathrm{t}} \mathrm{e}^{−\mathrm{t}} \frac{\mathrm{sinu}}{\mathrm{u}}\mathrm{du}\:\mathrm{dt} \\ $$

Question Number 45162 Answers: 0 Comments: 0

L{(t^2 +3t+2)H(t−1)+((sin 2t)/t)δ(t−(π/4))}

$$\mathrm{L}\left\{\left(\mathrm{t}^{\mathrm{2}} +\mathrm{3t}+\mathrm{2}\right)\mathrm{H}\left(\mathrm{t}−\mathrm{1}\right)+\frac{\mathrm{sin}\:\mathrm{2t}}{\mathrm{t}}\delta\left(\mathrm{t}−\frac{\pi}{\mathrm{4}}\right)\right\} \\ $$

Question Number 45160 Answers: 0 Comments: 0

L{(√(1+sin t))+∫_0 ^t cosht cost dt}

$$\mathrm{L}\left\{\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{t}}+\int_{\mathrm{0}} ^{\mathrm{t}} \mathrm{cosht}\:\mathrm{cost}\:\mathrm{dt}\right\} \\ $$

Question Number 45158 Answers: 0 Comments: 1

∫((e^(2x) −e^x +1)/((e^x sinx+cosx)(e^x cosx−sinx)))dx =?

$$\:\:\int\frac{{e}^{\mathrm{2}{x}} −{e}^{{x}} +\mathrm{1}}{\left({e}^{{x}} {sinx}+{cosx}\right)\left({e}^{{x}} {cosx}−{sinx}\right)}{dx}\:=? \\ $$

Question Number 45129 Answers: 1 Comments: 1

Question Number 45128 Answers: 1 Comments: 1

Question Number 45122 Answers: 0 Comments: 1

Question Number 45117 Answers: 1 Comments: 3

Prove that ∫_0 ^1 ((x^a −1)/(log x)) dx = log (a+1).

$${Prove}\:{that}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{x}^{{a}} −\mathrm{1}}{\mathrm{log}\:{x}}\:{dx}\:=\:\mathrm{log}\:\left({a}+\mathrm{1}\right). \\ $$

Question Number 45112 Answers: 0 Comments: 3

Question Number 45125 Answers: 1 Comments: 0

Question Number 45127 Answers: 1 Comments: 0

Question Number 45126 Answers: 0 Comments: 1

Question Number 45085 Answers: 1 Comments: 0

A motorist travelled from A to B. This is a distance of 142km at an average speed of 60kmhr^(−1) .He spent 5/2hours in B and then returned to A at an average speed of 80kmh^(−1) . a)At what time did the man arrive back at A b)find the average speed for the_ total journey.

$${A}\:{motorist}\:{travelled}\:{from}\:{A}\:{to}\:{B}. \\ $$$${This}\:{is}\:{a}\:{distance}\:{of}\:\mathrm{142}{km}\:{at}\:{an} \\ $$$${average}\:{speed}\:{of}\:\mathrm{60}{kmhr}^{−\mathrm{1}} .{He} \\ $$$${spent}\:\mathrm{5}/\mathrm{2}{hours}\:{in}\:{B}\:{and}\:{then} \\ $$$${returned}\:{to}\:{A}\:{at}\:{an}\:{average}\:{speed} \\ $$$${of}\:\mathrm{80}{kmh}^{−\mathrm{1}} . \\ $$$$\left.{a}\right){At}\:{what}\:{time}\:{did}\:{the}\:{man}\:{arrive} \\ $$$${back}\:{at}\:{A} \\ $$$$\left.{b}\right){find}\:{the}\:{average}\:{speed}\:{for}\:{the}_{} \\ $$$${total}\:{journey}. \\ $$

Question Number 45789 Answers: 2 Comments: 0

(18+5x)×3=309

$$ \\ $$$$\left(\mathrm{18}+\mathrm{5x}\right)×\mathrm{3}=\mathrm{309} \\ $$

Question Number 45082 Answers: 1 Comments: 1

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