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Question Number 114061 Answers: 1 Comments: 0

Question Number 114075 Answers: 2 Comments: 0

Question Number 114056 Answers: 4 Comments: 0

calculate ∫_2 ^(+∞) (dt/((2t+3)^4 (t−1)^5 ))

$$\mathrm{calculate}\:\int_{\mathrm{2}} ^{+\infty} \:\:\:\:\frac{\mathrm{dt}}{\left(\mathrm{2t}+\mathrm{3}\right)^{\mathrm{4}} \left(\mathrm{t}−\mathrm{1}\right)^{\mathrm{5}} } \\ $$

Question Number 114045 Answers: 4 Comments: 0

... advanced calculus... i : prove that :: ∫_0 ^( 1) ((ln(1+ln(1−x)))/(ln(1−x))) dx =^? Σ_(n=1) ^∞ ((Γ(n+1))/n^2 ) ii: prove that :: Ω =∫_0 ^( 1) ((ln(1+x))/(x(1+x^2 )))dx =^? ((5π^2 )/(48)) m.n.july 1970#

$$\:\:\:\:\:\:\:\:...\:\:{advanced}\:{calculus}... \\ $$$$ \\ $$$${i}\::\:\:{prove}\:\:{that}\::: \\ $$$$\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}+{ln}\left(\mathrm{1}−{x}\right)\right)}{{ln}\left(\mathrm{1}−{x}\right)}\:{dx}\:\overset{?} {=}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\Gamma\left({n}+\mathrm{1}\right)}{{n}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$${ii}:\: \\ $$$$\:\:\:\:{prove}\:{that}\::: \\ $$$$\:\:\:\:\:\:\:\Omega\:=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}+{x}\right)}{{x}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{dx}\:\overset{?} {=}\frac{\mathrm{5}\pi^{\mathrm{2}} }{\mathrm{48}} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.{july}\:\mathrm{1970}# \\ $$$$\:\:\: \\ $$

Question Number 114044 Answers: 1 Comments: 0

old and unanswered... Mr Mathdave??? ∫x^2 ln(1−x)ln(1+x)dx=?

$${old}\:{and}\:{unanswered}...\:{Mr}\:{Mathdave}??? \\ $$$$\int{x}^{\mathrm{2}} {ln}\left(\mathrm{1}−{x}\right){ln}\left(\mathrm{1}+{x}\right){dx}=? \\ $$

Question Number 114043 Answers: 1 Comments: 0

Σ_(n=1) ^∞ (1/(n^3 +1))

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{3}} +\mathrm{1}} \\ $$

Question Number 114037 Answers: 2 Comments: 0

∫^( (π/4)) _0 ((tan2x)/(sin2x+cos2x))dx

$$\underset{\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{4}}} \frac{{tan}\mathrm{2}{x}}{{sin}\mathrm{2}{x}+{cos}\mathrm{2}{x}}{dx} \\ $$

Question Number 114028 Answers: 4 Comments: 1

Question Number 114023 Answers: 2 Comments: 1

Σ_(n=1) ^∝ (1/(n^2 −1))=?

$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\propto} {\sum}}\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} −\mathrm{1}}=? \\ $$

Question Number 114032 Answers: 0 Comments: 0

Question Number 114020 Answers: 3 Comments: 0

lim_(d→∞) (√(6d)) cos ((2/( (√d)))) sin ((5/( (√d)))) ?

$$\underset{{d}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\mathrm{6}{d}}\:\mathrm{cos}\:\left(\frac{\mathrm{2}}{\:\sqrt{{d}}}\right)\:\mathrm{sin}\:\left(\frac{\mathrm{5}}{\:\sqrt{{d}}}\right)\:?\: \\ $$$$ \\ $$

Question Number 113997 Answers: 2 Comments: 0

Question Number 113996 Answers: 1 Comments: 1

Question Number 113991 Answers: 1 Comments: 1

If in a △ABC, ((a^2 −b^2 )/(a^2 +b^2 )) = ((sin (A−B))/(sin (A+B))) , then the triangle is

$$\mathrm{If}\:\:\mathrm{in}\:\mathrm{a}\:\bigtriangleup{ABC},\:\frac{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }\:=\:\frac{\mathrm{sin}\:\left({A}−{B}\right)}{\mathrm{sin}\:\left({A}+{B}\right)}\:, \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{is} \\ $$

Question Number 113989 Answers: 1 Comments: 0

Question Number 113986 Answers: 1 Comments: 0

The solution set of the equation 4 sin θ cos θ−2 cos θ−2 (√3) sin θ+(√3) =0 in the interval (0, 2π) is

$$\mathrm{The}\:\mathrm{solution}\:\mathrm{set}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{4}\:\mathrm{sin}\:\theta\:\mathrm{cos}\:\theta−\mathrm{2}\:\mathrm{cos}\:\theta−\mathrm{2}\:\sqrt{\mathrm{3}}\:\mathrm{sin}\:\theta+\sqrt{\mathrm{3}}\:=\mathrm{0} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{interval}\:\:\left(\mathrm{0},\:\mathrm{2}\pi\right)\:\:\mathrm{is} \\ $$

Question Number 113983 Answers: 2 Comments: 0

if Z_1 =1−i and Z_2 =i^4 by using demover find (Z_1 /Z_2 ) ?

$${if}\:{Z}_{\mathrm{1}} =\mathrm{1}−{i}\:{and}\:{Z}_{\mathrm{2}} ={i}^{\mathrm{4}} \:{by}\:{using}\:{demover}\:{find}\:\frac{{Z}_{\mathrm{1}} }{{Z}_{\mathrm{2}} }\:? \\ $$

Question Number 113981 Answers: 1 Comments: 0

The smallest positive root of the equation tan x−x=0, lies in

$$\mathrm{The}\:\mathrm{smallest}\:\mathrm{positive}\:\mathrm{root}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:\:\mathrm{tan}\:{x}−{x}=\mathrm{0},\:\mathrm{lies}\:\mathrm{in} \\ $$

Question Number 113976 Answers: 0 Comments: 1

A ball of mass 0.25kg is moving to the right at a speed of 7.4m/s. it strikes a wall at 90^0 and rebounds from the wall leaving it with a speed of 5.8n/s moving to the left. Find the direction and magnitude of the change in direction

$$\mathrm{A}\:\mathrm{ball}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{0}.\mathrm{25kg}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{to}\:\mathrm{the}\:\mathrm{right}\:\mathrm{at} \\ $$$$\mathrm{a}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{7}.\mathrm{4m}/\mathrm{s}.\:\mathrm{it}\:\mathrm{strikes}\:\mathrm{a}\:\mathrm{wall}\:\mathrm{at}\:\mathrm{90}^{\mathrm{0}} \mathrm{and}\: \\ $$$$\mathrm{rebounds}\:\mathrm{from}\:\mathrm{the}\:\mathrm{wall}\:\mathrm{leaving}\:\mathrm{it}\:\mathrm{with}\:\mathrm{a}\:\mathrm{speed} \\ $$$$\mathrm{of}\:\mathrm{5}.\mathrm{8n}/\mathrm{s}\:\mathrm{moving}\:\mathrm{to}\:\mathrm{the}\:\mathrm{left}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{direction}\: \\ $$$$\mathrm{and}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{the}\:\mathrm{change}\:\mathrm{in}\:\mathrm{direction} \\ $$

Question Number 113975 Answers: 1 Comments: 0

Find the nth term: 1, 0, − 1, 0, 1, 0, − 1, 0, ...

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}:\:\:\:\mathrm{1},\:\:\mathrm{0},\:\:−\:\mathrm{1},\:\:\mathrm{0},\:\:\mathrm{1},\:\:\mathrm{0},\:\:−\:\mathrm{1},\:\:\mathrm{0},\:\:... \\ $$

Question Number 113970 Answers: 0 Comments: 0