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Question Number 86062    Answers: 2   Comments: 1

∫((√(x^2 −25))/x)dx

$$\int\frac{\sqrt{{x}^{\mathrm{2}} −\mathrm{25}}}{{x}}{dx} \\ $$

Question Number 85982    Answers: 0   Comments: 2

A primitive of the function defned by f(x) = x −1 + (1/(x+1)) is A. F(x) = (x^2 /2) −x + ln(x + 1) B. F(x) = (x^2 /2) + ln(x−1) C. F(x) = (x^2 /2)−x + ln(1−x) D. F(x) = −x + ln(x−1)

$$\mathrm{A}\:\mathrm{primitive}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:\mathrm{defned}\:\mathrm{by}\:\mathrm{f}\left({x}\right)\:=\:{x}\:−\mathrm{1}\:+\:\frac{\mathrm{1}}{{x}+\mathrm{1}}\:\mathrm{is}\: \\ $$$$\mathrm{A}.\:\mathrm{F}\left({x}\right)\:=\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\:−{x}\:+\:\mathrm{ln}\left({x}\:+\:\mathrm{1}\right)\:\:\:\:\mathrm{B}.\:\mathrm{F}\left({x}\right)\:=\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\:+\:\mathrm{ln}\left({x}−\mathrm{1}\right) \\ $$$$\mathrm{C}.\:\mathrm{F}\left({x}\right)\:=\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}}−{x}\:+\:\mathrm{ln}\left(\mathrm{1}−{x}\right)\:\:\:\:\:\:\:\:\:\mathrm{D}.\:\mathrm{F}\left({x}\right)\:=\:−{x}\:+\:\mathrm{ln}\left({x}−\mathrm{1}\right) \\ $$$$ \\ $$

Question Number 85888    Answers: 0   Comments: 5

i−∫_0 ^5 (x+[2x])^([(x/3)]) dx ii−∫_0 ^3 (z−{z})^([z]) dz

$${i}−\int_{\mathrm{0}} ^{\mathrm{5}} \left({x}+\left[\mathrm{2}{x}\right]\right)^{\left[\frac{{x}}{\mathrm{3}}\right]} {dx} \\ $$$$ \\ $$$${ii}−\int_{\mathrm{0}} ^{\mathrm{3}} \left({z}−\left\{{z}\right\}\right)^{\left[{z}\right]} \:{dz} \\ $$

Question Number 85872    Answers: 1   Comments: 1

∫cos^(2020) x dx = ?

$$\int\mathrm{cos}^{\mathrm{2020}} \mathrm{x}\:\mathrm{dx}\:=\:? \\ $$

Question Number 85858    Answers: 0   Comments: 0

Is a matrix A^T A always positive definite?

$$\mathrm{Is}\:\mathrm{a}\:\mathrm{matrix} \\ $$$$\mathrm{A}^{\mathrm{T}} \mathrm{A}\:\mathrm{always}\:\mathrm{positive}\:\mathrm{definite}? \\ $$

Question Number 85698    Answers: 0   Comments: 0

please any recommendation of a youtube video on General conics??

$$\mathrm{please}\:\mathrm{any}\:\mathrm{recommendation}\:\mathrm{of}\:\mathrm{a}\:\mathrm{youtube}\:\mathrm{video} \\ $$$$\mathrm{on}\:\mathrm{General}\:\mathrm{conics}?? \\ $$

Question Number 85676    Answers: 0   Comments: 15

∫ _0 ^∞ (dx/((x+(√(1+x^2 )))^2 )) let x = tan t ⇒dx=sec^2 t dt ∫_0 ^(π/2) ((sec^2 t dt)/((tan t+sec t)^2 )) = ∫_0 ^(π/2) (dt/((sin t+1)^2 )) = ∫_0 ^(π/2) (dt/((cos (1/2)t+sin (1/2)t)^4 )) = ∫_0 ^(π/2) (dt/(4cos^4 ((1/2)t−(π/4)))) = (1/4)∫_0 ^(π/2) sec^4 ((1/2)t−(π/4)) dt [ let (1/2)t−(π/4)= u] = (1/4)∫_(−(π/4)) ^0 sec^4 u ×2du =(1/2)∫ _(−(π/4)) ^0 (tan^2 u+1) d(tan u) = (1/2) [(1/3)tan^3 u + tan u ]_(−(π/4)) ^0 = (1/2) [ 0−(−(1/3)−1)]= (2/3)

$$\int\underset{\mathrm{0}} {\overset{\infty} {\:}}\:\frac{{dx}}{\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)^{\mathrm{2}} } \\ $$$${let}\:{x}\:=\:\mathrm{tan}\:{t}\:\Rightarrow{dx}=\mathrm{sec}\:^{\mathrm{2}} {t}\:{dt} \\ $$$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{sec}\:^{\mathrm{2}} {t}\:{dt}}{\left(\mathrm{tan}\:{t}+\mathrm{sec}\:{t}\right)^{\mathrm{2}} }\:=\: \\ $$$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{{dt}}{\left(\mathrm{sin}\:{t}+\mathrm{1}\right)^{\mathrm{2}} }\:=\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{{dt}}{\left(\mathrm{cos}\:\frac{\mathrm{1}}{\mathrm{2}}{t}+\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{2}}{t}\right)^{\mathrm{4}} } \\ $$$$=\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{{dt}}{\mathrm{4cos}^{\mathrm{4}} \:\left(\frac{\mathrm{1}}{\mathrm{2}}{t}−\frac{\pi}{\mathrm{4}}\right)} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{4}}\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\mathrm{sec}\:^{\mathrm{4}} \left(\frac{\mathrm{1}}{\mathrm{2}}{t}−\frac{\pi}{\mathrm{4}}\right)\:{dt} \\ $$$$\left[\:{let}\:\frac{\mathrm{1}}{\mathrm{2}}{t}−\frac{\pi}{\mathrm{4}}=\:{u}\right] \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{4}}\underset{−\frac{\pi}{\mathrm{4}}} {\overset{\mathrm{0}} {\int}}\:\mathrm{sec}\:^{\mathrm{4}} {u}\:×\mathrm{2}{du} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int\underset{−\frac{\pi}{\mathrm{4}}} {\overset{\mathrm{0}} {\:}}\left(\mathrm{tan}\:^{\mathrm{2}} {u}+\mathrm{1}\right)\:{d}\left(\mathrm{tan}\:{u}\right) \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\:\left[\frac{\mathrm{1}}{\mathrm{3}}\mathrm{tan}\:^{\mathrm{3}} {u}\:+\:\mathrm{tan}\:{u}\:\right]_{−\frac{\pi}{\mathrm{4}}} ^{\mathrm{0}} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\:\left[\:\mathrm{0}−\left(−\frac{\mathrm{1}}{\mathrm{3}}−\mathrm{1}\right)\right]=\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$ \\ $$

Question Number 85580    Answers: 0   Comments: 0

Solve: (D^2 +2D+1)y= x cos x

$$\boldsymbol{\mathrm{Solve}}: \\ $$$$\:\left(\mathrm{D}^{\mathrm{2}} +\mathrm{2D}+\mathrm{1}\right)\mathrm{y}=\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x} \\ $$$$ \\ $$

Question Number 85354    Answers: 0   Comments: 0

∫x(sin(cos(x)))^(x−1) dx

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

Question Number 85286    Answers: 0   Comments: 2

Question Number 85279    Answers: 3   Comments: 0

who can help write out the mechanism for the reaction C_6 H_6 →_(HNO_3 ) ^(H_2 SO_4 ) C_6 H_5 NO_2

$$\mathrm{who}\:\mathrm{can}\:\mathrm{help}\:\mathrm{write}\:\mathrm{out}\:\mathrm{the}\:\mathrm{mechanism}\:\mathrm{for}\:\mathrm{the}\: \\ $$$$\mathrm{reaction} \\ $$$$\:\:\:\mathrm{C}_{\mathrm{6}} \mathrm{H}_{\mathrm{6}} \:\underset{\mathrm{HNO}_{\mathrm{3}} } {\overset{\mathrm{H}_{\mathrm{2}} \mathrm{SO}_{\mathrm{4}} } {\rightarrow}}\:\:\mathrm{C}_{\mathrm{6}} \mathrm{H}_{\mathrm{5}} \mathrm{NO}_{\mathrm{2}} \\ $$

Question Number 85262    Answers: 1   Comments: 6

find the centre of symmetry of the curve y = (1/(x + 2))

$$\mathrm{find}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{symmetry}\:\mathrm{of}\:\mathrm{the}\:\mathrm{curve} \\ $$$$\:\:\:{y}\:=\:\frac{\mathrm{1}}{{x}\:+\:\mathrm{2}} \\ $$

Question Number 85222    Answers: 0   Comments: 3

In C++ What is the sections doing ? and What is the output from the sections below ? a. int p=o; for (int i=1; i<=30; i++){ if (i%5==0) p+=i; } cout<<p<<endl; b. int count=2; int g=0; while (count<=50){ g=count; cout<<g<<endl; count +=2; } cout<<count<<endl;

$$\mathrm{In}\:\mathrm{C}++ \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sections}\:\mathrm{doing}\:?\:\mathrm{and} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{output}\:\mathrm{from}\:\mathrm{the}\:\mathrm{sections}\: \\ $$$$\mathrm{below}\:? \\ $$$$\mathrm{a}.\:\mathrm{int}\:\mathrm{p}=\mathrm{o}; \\ $$$$\:\:\:\:\:\mathrm{for}\:\left(\mathrm{int}\:\mathrm{i}=\mathrm{1};\:\mathrm{i}<=\mathrm{30};\:\mathrm{i}++\right)\left\{\right. \\ $$$$\:\:\:\:\:\mathrm{if}\:\left(\mathrm{i\%5}==\mathrm{0}\right) \\ $$$$\:\:\:\:\:\:\mathrm{p}+=\mathrm{i};\:\: \\ $$$$\left.\:\:\:\:\:\:\:\right\} \\ $$$$\:\:\:\:\:\:\:\mathrm{cout}<<\mathrm{p}<<\mathrm{endl}; \\ $$$$ \\ $$$$ \\ $$$$\mathrm{b}.\:\:\mathrm{int}\:\mathrm{count}=\mathrm{2}; \\ $$$$\:\:\:\:\:\:\mathrm{int}\:\mathrm{g}=\mathrm{0}; \\ $$$$\:\:\:\:\:\:\mathrm{while}\:\left(\mathrm{count}<=\mathrm{50}\right)\left\{\right. \\ $$$$\:\:\:\:\:\:\mathrm{g}=\mathrm{count}; \\ $$$$\:\:\:\:\:\:\mathrm{cout}<<\mathrm{g}<<\mathrm{endl}; \\ $$$$\:\:\:\:\:\:\mathrm{count}\:+=\mathrm{2}; \\ $$$$\left.\:\:\:\:\:\:\:\right\} \\ $$$$\:\:\:\:\:\:\:\mathrm{cout}<<\mathrm{count}<<\mathrm{endl}; \\ $$

Question Number 85142    Answers: 1   Comments: 0

show that ∫_0 ^n [x^2 ]dx =n(n^2 −1)−Σ_(k=1) ^(n^2 −1) (√k)

$${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{{n}} \left[{x}^{\mathrm{2}} \right]{dx}\:={n}\left({n}^{\mathrm{2}} −\mathrm{1}\right)−\underset{{k}=\mathrm{1}} {\overset{{n}^{\mathrm{2}} −\mathrm{1}} {\sum}}\sqrt{{k}}\: \\ $$

Question Number 85131    Answers: 0   Comments: 4

what procedure will you use to find the inverse of A = ((2,1,9),(1,5,1),(3,0,3) )

$$\mathrm{what}\:\mathrm{procedure}\:\mathrm{will}\:\mathrm{you}\:\mathrm{use}\:\mathrm{to}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{inverse}\:\mathrm{of} \\ $$$$\:\mathrm{A}\:=\:\begin{pmatrix}{\mathrm{2}}&{\mathrm{1}}&{\mathrm{9}}\\{\mathrm{1}}&{\mathrm{5}}&{\mathrm{1}}\\{\mathrm{3}}&{\mathrm{0}}&{\mathrm{3}}\end{pmatrix} \\ $$

Question Number 85129    Answers: 0   Comments: 2

lim_(x→e) [∫_0 ^e ((1/x))dx] =?

$$\underset{{x}\rightarrow{e}} {\mathrm{lim}}\:\left[\underset{\mathrm{0}} {\overset{{e}} {\int}}\left(\frac{\mathrm{1}}{{x}}\right){dx}\right]\:=? \\ $$

Question Number 85127    Answers: 1   Comments: 4

evaluate: lim_(x→0) (√x) ln(sin x)

$$\mathrm{evaluate}: \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\sqrt{{x}}\:\mathrm{ln}\left(\mathrm{sin}\:{x}\right) \\ $$$$ \\ $$

Question Number 85083    Answers: 0   Comments: 1

a^3 −b^3 =...?

$${a}^{\mathrm{3}} −{b}^{\mathrm{3}} =...? \\ $$

Question Number 85020    Answers: 0   Comments: 4

solve integration ∫_1 ^2 x d⌊x^2 ⌋

$${solve}\:{integration} \\ $$$$\int_{\mathrm{1}} ^{\mathrm{2}} {x}\:{d}\lfloor{x}^{\mathrm{2}} \rfloor \\ $$

Question Number 85003    Answers: 1   Comments: 7

x≤[x]<x+1 is that right if (x) was negative

$${x}\leqslant\left[{x}\right]<{x}+\mathrm{1} \\ $$$${is}\:{that}\:{right}\:{if}\:\left({x}\right)\:{was}\:{negative} \\ $$

Question Number 84997    Answers: 0   Comments: 2

log_(x/2) x^2 −log_(16x) x^3 +40log_(4x) (√x)=0

$${log}_{\frac{{x}}{\mathrm{2}}} {x}^{\mathrm{2}} −{log}_{\mathrm{16}{x}} {x}^{\mathrm{3}} +\mathrm{40}{log}_{\mathrm{4}{x}} \sqrt{{x}}=\mathrm{0} \\ $$

Question Number 84890    Answers: 0   Comments: 3

If we have : y = e^x What is : (d/dy)e^x = ... If we derivate with y... Please...

$$\mathrm{If}\:\mathrm{we}\:\mathrm{have}\::\:\:\:\:\:{y}\:=\:{e}^{{x}} \\ $$$$ \\ $$$${W}\mathrm{hat}\:\mathrm{is}\::\:\:\:\frac{\mathrm{d}}{\mathrm{d}{y}}{e}^{{x}} \:=\:... \\ $$$$ \\ $$$$\mathrm{If}\:\mathrm{we}\:\mathrm{derivate}\:\mathrm{with}\:{y}... \\ $$$$ \\ $$$$\mathrm{Please}... \\ $$

Question Number 84814    Answers: 0   Comments: 1

1.Finx

$$\mathrm{1}.{Finx} \\ $$

Question Number 84740    Answers: 1   Comments: 5

find the remainder when −18 is divided by 4

$$\mathrm{find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:−\mathrm{18}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{4} \\ $$

Question Number 84739    Answers: 1   Comments: 0

find the unit digit in the number 15^(1789) + 17^(1789) + 19^(1789)

$$\mathrm{find}\:\mathrm{the}\:\mathrm{unit}\:\mathrm{digit}\:\mathrm{in}\:\mathrm{the}\:\mathrm{number} \\ $$$$\:\mathrm{15}^{\mathrm{1789}} \:+\:\mathrm{17}^{\mathrm{1789}} \:+\:\mathrm{19}^{\mathrm{1789}} \\ $$

Question Number 84680    Answers: 1   Comments: 0

show that ∫_0 ^1 ∫_0 ^1 ∫_0 ^1 ((log(xyz))/((1+x^2 )(1+y^2 )(1+z^2 ))) dx dy dz=((−3π^2 G)/(16))

$${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \frac{{log}\left({xyz}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{y}^{\mathrm{2}} \right)\left(\mathrm{1}+{z}^{\mathrm{2}} \right)}\:{dx}\:{dy}\:{dz}=\frac{−\mathrm{3}\pi^{\mathrm{2}} {G}}{\mathrm{16}} \\ $$

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