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Question Number 60817    Answers: 4   Comments: 2

V=(4/3)š›‘R^3 prove

$$\boldsymbol{\mathrm{V}}=\frac{\mathrm{4}}{\mathrm{3}}\boldsymbol{\pi\mathrm{R}}^{\mathrm{3}} \:\:\:\boldsymbol{\mathrm{prove}} \\ $$

Question Number 60816    Answers: 1   Comments: 0

S=4š›‘R^2 prove

$$\boldsymbol{\mathrm{S}}=\mathrm{4}\boldsymbol{\pi\mathrm{R}}^{\mathrm{2}} \:\:\:\boldsymbol{\mathrm{prove}} \\ $$

Question Number 60814    Answers: 1   Comments: 0

find x given that 9^(sin^2 x) +9^(cos^2 x) =2

$${find}\:{x}\:{given}\:{that} \\ $$$$\mathrm{9}^{{sin}^{\mathrm{2}} {x}} +\mathrm{9}^{{cos}^{\mathrm{2}} {x}} =\mathrm{2}\: \\ $$$$ \\ $$

Question Number 60812    Answers: 0   Comments: 5

Question Number 60797    Answers: 0   Comments: 2

∫(e^w /w^(n+1) )dw, n∈N

$$\int\frac{{e}^{{w}} }{{w}^{{n}+\mathrm{1}} }{dw},\:{n}\in\mathbb{N} \\ $$

Question Number 60791    Answers: 1   Comments: 2

∫(e^n /x^(n+1) )dx, n∈N

$$\int\frac{{e}^{{n}} }{{x}^{{n}+\mathrm{1}} }{dx},\:\mathrm{n}\in\mathbb{N} \\ $$

Question Number 60788    Answers: 2   Comments: 1

Question Number 60783    Answers: 0   Comments: 2

∫_(āˆ’āˆž) ^āˆž sin((1/(1+x^2 ))) dx

$$\underset{āˆ’\infty} {\overset{\infty} {\int}}{sin}\left(\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\right)\:{dx} \\ $$

Question Number 60775    Answers: 0   Comments: 1

Question Number 60765    Answers: 0   Comments: 2

express in partial fraction 14/(x^2 +3)(x+2)

$${express}\:{in}\:{partial}\:{fraction}\:\mathrm{14}/\left({x}^{\mathrm{2}} +\mathrm{3}\right)\left({x}+\mathrm{2}\right) \\ $$

Question Number 60756    Answers: 1   Comments: 1

express in partial fraction 5/(xāˆ’2)(x+3)^2

$${express}\:{in}\:{partial}\:{fraction}\:\mathrm{5}/\left({x}āˆ’\mathrm{2}\right)\left({x}+\mathrm{3}\right)^{\mathrm{2}} \\ $$

Question Number 60748    Answers: 1   Comments: 1

Question Number 60745    Answers: 4   Comments: 5

Question Number 60739    Answers: 1   Comments: 4

evaluate i.∫ (((x+1)/(xāˆ’1)))dx ii. ∫_0 ^Ļ€ (2cosxsinx)dx iii. ∫_((Ļ€/(3 )) ) ^Ļ€ (((sin2x)/(cos2x)))dx

$${evaluate}\:\: \\ $$$${i}.\int\:\left(\frac{{x}+\mathrm{1}}{{x}āˆ’\mathrm{1}}\right){dx} \\ $$$${ii}.\:\:\int_{\mathrm{0}} ^{\pi} \left(\mathrm{2}{cosxsinx}\right){dx}\:\: \\ $$$${iii}.\:\:\int_{\frac{\pi}{\mathrm{3}\:}\:} ^{\pi} \left(\frac{{sin}\mathrm{2}{x}}{{cos}\mathrm{2}{x}}\right){dx} \\ $$

Question Number 60735    Answers: 3   Comments: 0

express in partial fraction 3/(x+1)(x^2 āˆ’4)

$${express}\:{in}\:{partial}\:{fraction}\:\mathrm{3}/\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} āˆ’\mathrm{4}\right) \\ $$

Question Number 60734    Answers: 1   Comments: 4

Find the product of the real roots of the equation (x + 2 + (√(x^2 + 4x + 3)))^5 āˆ’ 32(x + 2 āˆ’ (√(x^2 + 4x + 3)))^5 = 31

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{the}\:\mathrm{real}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:\:\:\:\:\:\:\:\:\left(\mathrm{x}\:+\:\mathrm{2}\:+\:\sqrt{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4x}\:+\:\mathrm{3}}\right)^{\mathrm{5}} \:āˆ’\:\:\mathrm{32}\left(\mathrm{x}\:+\:\mathrm{2}\:āˆ’\:\sqrt{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4x}\:+\:\mathrm{3}}\right)^{\mathrm{5}} \:\:=\:\:\mathrm{31} \\ $$

Question Number 60731    Answers: 0   Comments: 0

Question Number 60728    Answers: 0   Comments: 0

calculate ∫_1 ^(+āˆž) ((ln(lnx))/(x^2 āˆ’x +1))dx

$${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{ln}\left({lnx}\right)}{{x}^{\mathrm{2}} āˆ’{x}\:+\mathrm{1}}{dx} \\ $$

Question Number 60727    Answers: 0   Comments: 2

calculate ∫_1 ^(+āˆž) ((ln(lnx))/(1+x^2 ))dx

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

Question Number 60725    Answers: 0   Comments: 2

x = Ī£_(0≤i≤j≤2019) ( _( j)^(2019) )( _i^j )

$${x}\:\:=\:\:\underset{\mathrm{0}\leqslant{i}\leqslant{j}\leqslant\mathrm{2019}} {\sum}\:\left(\:_{\:\:\:\:{j}} ^{\mathrm{2019}} \:\right)\left(\:\:_{{i}} ^{{j}} \:\:\right)\: \\ $$

Question Number 60723    Answers: 0   Comments: 8

solve for x (√(aāˆ’(√(a+x)))) + (√(a+(√(aāˆ’x)))) = 2x

$${solve}\:{for}\:{x}\: \\ $$$$\sqrt{{a}āˆ’\sqrt{{a}+{x}}}\:+\:\sqrt{{a}+\sqrt{{a}āˆ’{x}}}\:=\:\mathrm{2}{x} \\ $$

Question Number 60717    Answers: 0   Comments: 1

Question Number 60706    Answers: 0   Comments: 2

let f(x) =(√(1+x^2 )) 1) let U_n =f^((n)) (x) prove that Ī£_(k=0) ^n C_n ^k U_k U_(n+1āˆ’k) =0 for n≄2 2) developp f at integr serie .

$${let}\:{f}\left({x}\right)\:=\sqrt{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{let}\:{U}_{{n}} ={f}^{\left({n}\right)} \left({x}\right)\:\:{prove}\:{that}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{U}_{{k}} {U}_{{n}+\mathrm{1}āˆ’{k}} =\mathrm{0}\:\:{for}\:{n}\geqslant\mathrm{2} \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$

Question Number 60705    Answers: 1   Comments: 0

Question Number 60716    Answers: 1   Comments: 1

Question Number 60702    Answers: 0   Comments: 0

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