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Question Number 92137 Answers: 0 Comments: 2

∫((2x)/(1+x))

$$\int\frac{\mathrm{2}{x}}{\mathrm{1}+{x}} \\ $$

Question Number 92135 Answers: 0 Comments: 5

a^x = log _a (x) a=?

$${a}^{{x}} \:=\:\mathrm{log}\:_{{a}} \:\left({x}\right) \\ $$$${a}=? \\ $$

Question Number 92134 Answers: 0 Comments: 1

find ∫_(−1) ^1 (e^x /(√(1−x^2 )))dx

$${find}\:\int_{−\mathrm{1}} ^{\mathrm{1}} \:\frac{{e}^{{x}} }{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx}\: \\ $$

Question Number 92133 Answers: 0 Comments: 0

1) decompose F(x) =(1/(x^5 −1)) 2) calculate ∫_2 ^(+∞) (dx/(x^5 −1))

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

Question Number 92126 Answers: 0 Comments: 0

∫ (√((x^2 +2x−1)/(x+1))) dx

$$\int\:\sqrt{\frac{{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{1}}{{x}+\mathrm{1}}}\:{dx}\: \\ $$

Question Number 92120 Answers: 0 Comments: 0

∫_(−3) ^4 ⌊x.⌈x^2 ⌉⌋ dx

$$\int_{−\mathrm{3}} ^{\mathrm{4}} \lfloor{x}.\lceil{x}^{\mathrm{2}} \rceil\rfloor\:{dx} \\ $$

Question Number 92119 Answers: 0 Comments: 3

show that ∫_1 ^∞ (1/(⌊x⌋^2 ))dx=∫_0 ^1 ∫_0 ^1 ((dx dy)/(1−xy))

$${show}\:{that}\: \\ $$$$\int_{\mathrm{1}} ^{\infty} \frac{\mathrm{1}}{\lfloor{x}\rfloor^{\mathrm{2}} }{dx}=\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}\:{dy}}{\mathrm{1}−{xy}} \\ $$

Question Number 92118 Answers: 1 Comments: 3

If 9^(2x+1 ) = ((81^(x−2) )/(3x)) . find x

$$\mathrm{If}\:\:\mathrm{9}^{\mathrm{2x}+\mathrm{1}\:\:\:} =\:\:\frac{\mathrm{81}^{\mathrm{x}−\mathrm{2}} }{\mathrm{3x}}\:\:.\:\:\:\:\:\:\:\:\:\:\:\mathrm{find}\:\mathrm{x} \\ $$

Question Number 92117 Answers: 0 Comments: 3

solve for x and y if: (√x)+y=11 and x+(√y)=7

$$\mathrm{solve}\:\mathrm{for}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{if}: \\ $$$$\sqrt{\mathrm{x}}+\mathrm{y}=\mathrm{11}\:\:\:\:\mathrm{and}\:\:\:\:\mathrm{x}+\sqrt{\mathrm{y}}=\mathrm{7} \\ $$

Question Number 92116 Answers: 0 Comments: 0

what is the super hexagon?

$${what}\:{is}\:{the}\:{super}\:{hexagon}? \\ $$

Question Number 92115 Answers: 1 Comments: 0

Question Number 92114 Answers: 1 Comments: 0

Question Number 92102 Answers: 2 Comments: 3

how can we factorize x^5 −1 ?

$${how}\:{can}\:{we}\:{factorize}\:\:\:{x}^{\mathrm{5}} −\mathrm{1}\:\:? \\ $$

Question Number 92089 Answers: 0 Comments: 0

calculate ∫_0 ^(π/4) ln(cosx+sinx)dx

$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left({cosx}+{sinx}\right){dx} \\ $$

Question Number 92088 Answers: 0 Comments: 0

calculate ∫_0 ^(π/4) ln(cosx) and ∫_0 ^(π/4) ln(sinx)dx

$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left({cosx}\right)\:\:{and}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{ln}\left({sinx}\right){dx} \\ $$

Question Number 92087 Answers: 0 Comments: 1

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

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

Question Number 92086 Answers: 0 Comments: 0

f and g are two continous function on R find we suppose f and g odd determine lim_(x→0) ((gof(x)−fog(x))/x)

$${f}\:{and}\:{g}\:{are}\:{two}\:{continous}\:{function}\:{on}\:{R}\:{find} \\ $$$${we}\:{suppose}\:{f}\:{and}\:{g}\:{odd}\:\:{determine}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\frac{{gof}\left({x}\right)−{fog}\left({x}\right)}{{x}} \\ $$

Question Number 92084 Answers: 1 Comments: 0

Question Number 92082 Answers: 1 Comments: 2

let f(α) =∫_0 ^1 x(√(x^2 −x+α))dx with α>(1/4) 1) explicit f(α) 2) calculate g(α) =∫_0 ^1 ((xdx)/(√(x^2 −x+α))) 3) find the value of intehrals ∫_0 ^1 x(√(x^2 −x+(√2)))dx snd ∫_0 ^1 ((xdx)/(√(x^2 −x+(√2))))

$${let}\:{f}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {x}\sqrt{{x}^{\mathrm{2}} −{x}+\alpha}{dx}\:\:\:\:\:\:{with}\:\alpha>\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\left.\mathrm{1}\right)\:{explicit}\:\:{f}\left(\alpha\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{xdx}}{\sqrt{{x}^{\mathrm{2}} −{x}+\alpha}} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:{intehrals}\:\int_{\mathrm{0}} ^{\mathrm{1}} {x}\sqrt{{x}^{\mathrm{2}} −{x}+\sqrt{\mathrm{2}}}{dx}\:{snd} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{xdx}}{\sqrt{{x}^{\mathrm{2}} −{x}+\sqrt{\mathrm{2}}}} \\ $$

Question Number 92081 Answers: 0 Comments: 0

find ∫_0 ^1 (x^3 −3)(√(x^2 +2x+5))dx

$${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \left({x}^{\mathrm{3}} −\mathrm{3}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{5}}{dx} \\ $$

Question Number 92080 Answers: 0 Comments: 0

calculate lim_(x→0) ((sin(2shx) −sh(2sinx))/(e^x −1))

$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{{sin}\left(\mathrm{2}{shx}\right)\:−{sh}\left(\mathrm{2}{sinx}\right)}{{e}^{{x}} −\mathrm{1}} \\ $$

Question Number 92079 Answers: 0 Comments: 1

find lim_(x→0) ((e^(sin^2 x) −e^(x^3 −2x) )/x^2 )

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{e}^{{sin}^{\mathrm{2}} {x}} −{e}^{{x}^{\mathrm{3}} −\mathrm{2}{x}} }{{x}^{\mathrm{2}} } \\ $$

Question Number 92078 Answers: 0 Comments: 2

calculate ∫_(−∞) ^(+∞) ((cos(arctan(2x+1)))/(x^2 +x+1))dx

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

Question Number 92056 Answers: 0 Comments: 2

lim_(x→0^+ ) ((ln(x))/(cot x))

$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\mathrm{ln}\left({x}\right)}{\mathrm{cot}\:{x}} \\ $$

Question Number 92055 Answers: 0 Comments: 3

∫(((x+1)/((x^2 +4x+5)^2 )))dx

$$\int\left(\frac{\mathrm{x}+\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{4x}+\mathrm{5}\right)^{\mathrm{2}} }\right)\mathrm{dx} \\ $$

Question Number 92054 Answers: 0 Comments: 0

tan^2 ((π/7))+tan^2 (((2π)/7))+tan^2 (((3π)/7)) ?

$$\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\pi}{\mathrm{7}}\right)+\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)+\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)\:? \\ $$

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