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Question Number 88360 Answers: 0 Comments: 2

(e/(√e)) × ((e)^(1/(3 )) /(e)^(1/(4 )) ) × ((e)^(1/(5 )) /(e)^(1/(6 )) ) × ((e)^(1/(7 )) /(e)^(1/(8 )) )×...=?

$$\frac{\mathrm{e}}{\sqrt{\mathrm{e}}}\:×\:\frac{\sqrt[{\mathrm{3}\:\:}]{\mathrm{e}}}{\sqrt[{\mathrm{4}\:\:}]{\mathrm{e}}}\:×\:\frac{\sqrt[{\mathrm{5}\:\:}]{\mathrm{e}}}{\sqrt[{\mathrm{6}\:\:}]{\mathrm{e}}}\:×\:\frac{\sqrt[{\mathrm{7}\:\:}]{\mathrm{e}}}{\sqrt[{\mathrm{8}\:\:}]{\mathrm{e}}}×...=? \\ $$

Question Number 88357 Answers: 0 Comments: 1

∫ _1 ^4 (dx/((4x−1)(√x)))

$$\int\underset{\mathrm{1}} {\overset{\mathrm{4}} {\:}}\:\frac{\mathrm{dx}}{\left(\mathrm{4x}−\mathrm{1}\right)\sqrt{\mathrm{x}}} \\ $$

Question Number 88352 Answers: 1 Comments: 1

Question Number 88349 Answers: 1 Comments: 1

Question Number 88339 Answers: 3 Comments: 3

∫( (√(tan x )) + (√(cot x)) )dx = ?

$$\:\int\left(\:\sqrt{\mathrm{tan}\:{x}\:}\:+\:\sqrt{\mathrm{cot}\:{x}}\:\right){dx}\:=\:? \\ $$

Question Number 88329 Answers: 0 Comments: 4

Question Number 88332 Answers: 0 Comments: 0

Question Number 88314 Answers: 2 Comments: 1

( a,b )are complex numbers and a^2 +ab+b^2 =0 find ((a/(a+b)))^(2020) +((b/(a+b)))^(2020)

$$\left(\:{a},{b}\:\right){are}\:{complex}\:{numbers}\:{and}\:{a}^{\mathrm{2}} +{ab}+{b}^{\mathrm{2}} =\mathrm{0} \\ $$$${find}\:\left(\frac{{a}}{{a}+{b}}\right)^{\mathrm{2020}} +\left(\frac{{b}}{{a}+{b}}\right)^{\mathrm{2020}} \\ $$$$ \\ $$

Question Number 88310 Answers: 1 Comments: 1

Question Number 88306 Answers: 0 Comments: 5

Question Number 88301 Answers: 0 Comments: 2

A circle touches the four sides of quadrilateral ABCD. Show/prove that AB+CD=BC+DA. Please help.

$${A}\:{circle}\:{touches}\:{the}\:{four}\:{sides} \\ $$$${of}\:{quadrilateral}\:{ABCD}.\:\mathrm{Show}/\mathrm{prove} \\ $$$$\mathrm{that}\:\mathrm{A}{B}+{CD}={BC}+{DA}. \\ $$$$\mathrm{Please}\:\mathrm{help}. \\ $$

Question Number 88300 Answers: 0 Comments: 0

A circle touches the four sides of quadrilateral ABCD. Show/prove that AB+CD=BC+DA. Please help.

$${A}\:{circle}\:{touches}\:{the}\:{four}\:{sides} \\ $$$${of}\:{quadrilateral}\:{ABCD}.\:\mathrm{Show}/\mathrm{prove} \\ $$$$\mathrm{that}\:\mathrm{A}{B}+{CD}={BC}+{DA}. \\ $$$$\mathrm{Please}\:\mathrm{help}. \\ $$

Question Number 88307 Answers: 1 Comments: 0

∫(x^2 /(x^2 −(5/2)x−(3/2))) dx

$$\int\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} −\frac{\mathrm{5}}{\mathrm{2}}{x}−\frac{\mathrm{3}}{\mathrm{2}}}\:{dx} \\ $$

Question Number 88289 Answers: 0 Comments: 5

Question Number 88288 Answers: 1 Comments: 1

Question Number 88286 Answers: 0 Comments: 1

Question Number 88272 Answers: 1 Comments: 1

Question Number 88270 Answers: 0 Comments: 1

Question Number 88263 Answers: 1 Comments: 1

prove that ∣((e^z −e^(−z) )/2)∣^2 +cos^2 y=sinh^2 x when z=x+iy

$${prove}\:{that}\: \\ $$$$\mid\frac{{e}^{{z}} −{e}^{−{z}} }{\mathrm{2}}\mid^{\mathrm{2}} +{cos}^{\mathrm{2}} {y}={sinh}^{\mathrm{2}} {x}\:\:\:\:\:{when}\:{z}={x}+{iy} \\ $$$$ \\ $$

Question Number 88261 Answers: 1 Comments: 0

Question Number 88253 Answers: 0 Comments: 0

∫ ((ln(x^2 +1) dx)/(x+1))

$$\int\:\frac{\mathrm{ln}\left({x}^{\mathrm{2}} +\mathrm{1}\right)\:{dx}}{{x}+\mathrm{1}}\: \\ $$

Question Number 88252 Answers: 0 Comments: 0

Question Number 88251 Answers: 0 Comments: 0

Question Number 88245 Answers: 2 Comments: 0

Question Number 88240 Answers: 1 Comments: 3

Question Number 88239 Answers: 0 Comments: 0

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