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Question Number 93005 Answers: 1 Comments: 0

∫ sec x (√(sec x+tan x)) dx =

$$\int\:\mathrm{sec}\:\mathrm{x}\:\sqrt{\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\:=\: \\ $$

Question Number 93003 Answers: 1 Comments: 0

(x^2 −2xy−y^2 )dx−(x−y)^2 dy=0

$$\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2xy}−\mathrm{y}^{\mathrm{2}} \right)\mathrm{dx}−\left(\mathrm{x}−\mathrm{y}\right)^{\mathrm{2}} \:\mathrm{dy}=\mathrm{0} \\ $$

Question Number 92997 Answers: 1 Comments: 0

Question Number 92993 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) ((cos(cosx−sinx))/(x^2 +4))dx

$${calculate}\:\:\int_{−\infty} ^{+\infty} \:\frac{{cos}\left({cosx}−{sinx}\right)}{{x}^{\mathrm{2}} \:+\mathrm{4}}{dx} \\ $$

Question Number 92987 Answers: 2 Comments: 0

{ (((√y) + ln (x^2 )=2)),((y + 4 ln(x) =28)) :}

$$\begin{cases}{\sqrt{\mathrm{y}}\:+\:\mathrm{ln}\:\left(\mathrm{x}^{\mathrm{2}} \right)=\mathrm{2}}\\{\mathrm{y}\:+\:\mathrm{4}\:\mathrm{ln}\left(\mathrm{x}\right)\:=\mathrm{28}}\end{cases} \\ $$

Question Number 93004 Answers: 0 Comments: 0

∫ ((sin^(−1) (sin (x)))/(sin^4 (x)+cos^2 (x))) dx ?

$$\int\:\frac{\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\:\left(\mathrm{x}\right)\right)}{\mathrm{sin}\:^{\mathrm{4}} \left(\mathrm{x}\right)+\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{x}\right)}\:\mathrm{dx}\:? \\ $$

Question Number 92980 Answers: 1 Comments: 0

log _((9x))^(1/(3 )) ((√(x^3 /3))) + log _((3x^2 ))^(1/(3 )) ((√(27x))) ≤ 3

$$\mathrm{log}\:_{\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}{x}}} \:\left(\sqrt{\frac{{x}^{\mathrm{3}} }{\mathrm{3}}}\right)\:+\:\mathrm{log}\:_{\sqrt[{\mathrm{3}\:\:}]{\mathrm{3}{x}^{\mathrm{2}} }} \left(\sqrt{\mathrm{27}{x}}\right)\:\leqslant\:\mathrm{3} \\ $$

Question Number 92976 Answers: 1 Comments: 0

define Δ_n =((n(1+n))/2) find a closer form for Σ_(n=1) ^∞ (1/Δ_n ^m )

$${define} \\ $$$$\Delta_{{n}} =\frac{{n}\left(\mathrm{1}+{n}\right)}{\mathrm{2}} \\ $$$${find}\:{a}\:{closer}\:{form}\:{for} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\Delta_{{n}} ^{{m}} } \\ $$

Question Number 92971 Answers: 0 Comments: 3

1) decompose F(x) =(1/(x^4 (x−3)^5 )) 2)calculate ∫_5 ^(+∞) (dx/(x^4 (x−3)^5 ))

$$\left.\mathrm{1}\right)\:{decompose}\:{F}\left({x}\right)\:=\frac{\mathrm{1}}{{x}^{\mathrm{4}} \left({x}−\mathrm{3}\right)^{\mathrm{5}} } \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{5}} ^{+\infty} \:\frac{{dx}}{{x}^{\mathrm{4}} \left({x}−\mathrm{3}\right)^{\mathrm{5}} } \\ $$

Question Number 92966 Answers: 0 Comments: 3

lim_(x→−∞) ((6x+5)/(√(9x^2 +4x−2))) ?

$$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\frac{\mathrm{6x}+\mathrm{5}}{\sqrt{\mathrm{9x}^{\mathrm{2}} +\mathrm{4x}−\mathrm{2}}}\:? \\ $$

Question Number 92960 Answers: 2 Comments: 0

∫ ((sin^2 x dx)/((1+cos x)^2 ))

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

Question Number 92957 Answers: 0 Comments: 12

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Question Number 92952 Answers: 0 Comments: 1

∫_(−2) ^2 x^3 (cos((x/2))+(1/2))(√(4−x^2 )) dx

$$\int_{−\mathrm{2}} ^{\mathrm{2}} {x}^{\mathrm{3}} \left({cos}\left(\frac{{x}}{\mathrm{2}}\right)+\frac{\mathrm{1}}{\mathrm{2}}\right)\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }\:{dx} \\ $$

Question Number 92949 Answers: 1 Comments: 2

∫(1/x)sin((1/x)) dx

$$\int\frac{\mathrm{1}}{\mathrm{x}}\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:\mathrm{dx} \\ $$

Question Number 92940 Answers: 0 Comments: 0

prove that Γ(x).Γ(1−x) =(π/(sin(πx))) with 0<x<1

$${prove}\:{that}\:\Gamma\left({x}\right).\Gamma\left(\mathrm{1}−{x}\right)\:=\frac{\pi}{{sin}\left(\pi{x}\right)}\:\:{with}\:\mathrm{0}<{x}<\mathrm{1} \\ $$

Question Number 92939 Answers: 0 Comments: 0

find ∫_0 ^1 ((xlnx)/((x^2 +1)^2 ))dx

$${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{xlnx}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 92938 Answers: 1 Comments: 0

find ∫ (dx/((1+cosx)(3−sin^2 x)))

$${find}\:\int\:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{cosx}\right)\left(\mathrm{3}−{sin}^{\mathrm{2}} {x}\right)} \\ $$

Question Number 92937 Answers: 2 Comments: 1

find ∫_0 ^(2π) (dx/(3cosx +2))

$${find}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{{dx}}{\mathrm{3}{cosx}\:+\mathrm{2}} \\ $$

Question Number 92936 Answers: 2 Comments: 2

find ∫_0 ^(2π) (dx/(cosx +sinx))

$${find}\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{dx}}{{cosx}\:+{sinx}} \\ $$

Question Number 92935 Answers: 0 Comments: 0

calculate ∫_0 ^∞ (((x^2 −3)dx)/((x^2 −x+1)^2 ))

$${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{\left({x}^{\mathrm{2}} −\mathrm{3}\right){dx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 92934 Answers: 0 Comments: 0

calculate ∫_0 ^1 ((xlnx)/((x+1)^2 ))dx

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

Question Number 92933 Answers: 0 Comments: 0

prove thst for z∈C−Z (((πz)/(sin(πz))))^2 =Σ_(n=−∞) ^(+∞) (1/((z−n)^2 )) and (((πz)^2 )/(sin^2 (πz)))cos(πz) =Σ_(n=−∞) ^(+∞) (((−1)^n )/((z−n)^2 ))

$${prove}\:{thst}\:{for}\:{z}\in{C}−{Z}\:\:\:\:\:\left(\frac{\pi{z}}{{sin}\left(\pi{z}\right)}\right)^{\mathrm{2}} \:=\sum_{{n}=−\infty} ^{+\infty} \:\frac{\mathrm{1}}{\left({z}−{n}\right)^{\mathrm{2}} } \\ $$$${and}\:\:\frac{\left(\pi{z}\right)^{\mathrm{2}} }{{sin}^{\mathrm{2}} \left(\pi{z}\right)}{cos}\left(\pi{z}\right)\:=\sum_{{n}=−\infty} ^{+\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left({z}−{n}\right)^{\mathrm{2}} } \\ $$

Question Number 92925 Answers: 0 Comments: 4

S_n =Σ_(k=1) ^∞ (1/((4k^2 −1)^n )) find a simpler form

$${S}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{4}{k}^{\mathrm{2}} −\mathrm{1}\right)^{{n}} } \\ $$$${find}\:{a}\:{simpler}\:{form} \\ $$

Question Number 92923 Answers: 1 Comments: 0

Solve 1+(x/(2!))+(x^2 /(4!))+(x^3 /(6!))+∙∙∙ =0

$$\mathrm{Solve} \\ $$$$\mathrm{1}+\frac{\mathrm{x}}{\mathrm{2}!}+\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{4}!}+\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{6}!}+\centerdot\centerdot\centerdot\:=\mathrm{0} \\ $$

Question Number 92921 Answers: 0 Comments: 2

what is string theory

$${what}\:{is}\:{string}\:{theory} \\ $$

Question Number 92910 Answers: 2 Comments: 2

∫(dt/(3sint+4cost))

$$\int\frac{\mathrm{dt}}{\mathrm{3sint}+\mathrm{4cost}} \\ $$

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