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Question Number 172575 Answers: 0 Comments: 0

Question Number 172564 Answers: 2 Comments: 0

find ∫_0 ^1 (√x)(√(1−(√x)))lnx dx

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}}\sqrt{\mathrm{1}−\sqrt{{x}}}{lnx}\:{dx} \\ $$

Question Number 172560 Answers: 2 Comments: 1

prove for n∈N and n>1 (((n+1)/3))^n <n!<(((n+1)/2))^n

$${prove}\:{for}\:{n}\in{N}\:{and}\:{n}>\mathrm{1} \\ $$$$\left(\frac{{n}+\mathrm{1}}{\mathrm{3}}\right)^{{n}} <{n}!<\left(\frac{{n}+\mathrm{1}}{\mathrm{2}}\right)^{{n}} \\ $$

Question Number 172558 Answers: 1 Comments: 0

Question Number 172556 Answers: 3 Comments: 0

∫_ ln(1+x^2 )dx

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

Question Number 172555 Answers: 3 Comments: 3

∫_(1/5) ^5 ((arctan (x))/x) dx =?

$$\:\:\:\:\:\:\underset{\mathrm{1}/\mathrm{5}} {\overset{\mathrm{5}} {\int}}\:\frac{\mathrm{arctan}\:\left({x}\right)}{{x}}\:{dx}\:=? \\ $$

Question Number 181375 Answers: 1 Comments: 2

If a = 1, b = 2, c = 3, ... z = 26 then (t − a)(t − b)(t − c) ... (t − y)(t − z) = ??

$$\mathrm{If}\:\:\mathrm{a}\:=\:\mathrm{1},\:\mathrm{b}\:=\:\mathrm{2},\:\mathrm{c}\:=\:\mathrm{3},\:...\:\mathrm{z}\:\:=\:\:\mathrm{26} \\ $$$$\mathrm{then}\:\:\:\:\left(\mathrm{t}\:−\:\mathrm{a}\right)\left(\mathrm{t}\:−\:\mathrm{b}\right)\left(\mathrm{t}\:−\:\mathrm{c}\right)\:...\:\left(\mathrm{t}\:−\:\mathrm{y}\right)\left(\mathrm{t}\:−\:\mathrm{z}\right)\:=\:\:\:?? \\ $$

Question Number 181331 Answers: 1 Comments: 0

Solve: (dy/dx)=e^x (sinx)(y+1) y(2)=−1 .

$$\mathrm{Solve}: \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{e}^{\mathrm{x}} \left(\mathrm{sinx}\right)\left(\mathrm{y}+\mathrm{1}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{2}\right)=−\mathrm{1} \\ $$$$ \\ $$$$. \\ $$

Question Number 181329 Answers: 1 Comments: 0

Question Number 181330 Answers: 1 Comments: 0

Solve: (dy/dx)+2x(y+1)=0, y(0)=2

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

Question Number 172551 Answers: 0 Comments: 0

Question Number 172545 Answers: 1 Comments: 1

calcul Σ_(n=1) ^(+oo) (((−1)^n )/n)x^n

$${calcul} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{+{oo}} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}}{x}^{{n}} \\ $$

Question Number 172532 Answers: 2 Comments: 0

Question Number 172531 Answers: 4 Comments: 1

Question Number 172526 Answers: 1 Comments: 0

Ω=∫_0 ^( ∞) (( dx)/((4−2x+x^( 2) )^( 3) )) =^? (1/(64)) +(π/(36(√3)))

$$ \\ $$$$\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \frac{\:{dx}}{\left(\mathrm{4}−\mathrm{2}{x}+{x}^{\:\mathrm{2}} \right)^{\:\mathrm{3}} }\:\overset{?} {=}\:\frac{\mathrm{1}}{\mathrm{64}}\:+\frac{\pi}{\mathrm{36}\sqrt{\mathrm{3}}} \\ $$

Question Number 172520 Answers: 0 Comments: 1

Question Number 172519 Answers: 0 Comments: 1

Question Number 172516 Answers: 0 Comments: 1

solve x^2 =16^x

$${solve} \\ $$$${x}^{\mathrm{2}} =\mathrm{16}^{{x}} \\ $$

Question Number 172515 Answers: 1 Comments: 0

simplify ((z^2 −1)/(z−1))÷(1/(z^2 +1))×(1/(z+(1/z)))

$${simplify} \\ $$$$\frac{{z}^{\mathrm{2}} −\mathrm{1}}{{z}−\mathrm{1}}\boldsymbol{\div}\frac{\mathrm{1}}{{z}^{\mathrm{2}} +\mathrm{1}}×\frac{\mathrm{1}}{{z}+\frac{\mathrm{1}}{{z}}} \\ $$

Question Number 172514 Answers: 0 Comments: 0

if y=bcoslog((x/n))^n then (dy/dx)=??

$${if}\:{y}={bcoslog}\left(\frac{{x}}{{n}}\right)^{{n}} \\ $$$${then}\:\frac{{dy}}{{dx}}=?? \\ $$

Question Number 172513 Answers: 2 Comments: 2

simplify (√(a^2 b+b^3 +2ab^2 )) −(√(a^2 b+4b^3 +4ab^3 ))

$${simplify} \\ $$$$\sqrt{{a}^{\mathrm{2}} {b}+{b}^{\mathrm{3}} +\mathrm{2}{ab}^{\mathrm{2}} }\:−\sqrt{{a}^{\mathrm{2}} {b}+\mathrm{4}{b}^{\mathrm{3}} +\mathrm{4}{ab}^{\mathrm{3}} } \\ $$

Question Number 172511 Answers: 1 Comments: 0

solve: (a+b−2c)x^2 +(2a−b−c)x+(c+a−2b)=0

$${solve}: \\ $$$$\left({a}+{b}−\mathrm{2}{c}\right){x}^{\mathrm{2}} +\left(\mathrm{2}{a}−{b}−{c}\right){x}+\left({c}+{a}−\mathrm{2}{b}\right)=\mathrm{0} \\ $$

Question Number 172510 Answers: 1 Comments: 0

Question Number 172509 Answers: 2 Comments: 2

Question Number 172504 Answers: 2 Comments: 0

Question Number 172498 Answers: 0 Comments: 0

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