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Question Number 156229 Answers: 0 Comments: 4

∫_0 ^( (π/4)) ln(sin(2x)+cos(3x)) dx

$$\: \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \:\mathrm{ln}\left(\mathrm{sin}\left(\mathrm{2}{x}\right)+\mathrm{cos}\left(\mathrm{3}{x}\right)\right)\:{dx} \\ $$$$\: \\ $$

Question Number 156228 Answers: 1 Comments: 0

∫_0 ^( 1) ((log^3 (1−x^2 ))/x^3 ) dx

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

Question Number 156224 Answers: 0 Comments: 1

∫_0 ^( 1) (1/( (√(ln(x^2 )+1)) )) dx

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

Question Number 156222 Answers: 0 Comments: 1

∫_0 ^( 1) ln((sin(x)cos(x))^2 +1) dx

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

Question Number 156218 Answers: 1 Comments: 4

∫_0 ^( 1) (1/( (√(x(√(x^2 (√(x^3 (√(x^4 +1)))))))) )) dx

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{1}}{\:\sqrt{{x}\sqrt{{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{3}} \sqrt{{x}^{\mathrm{4}} +\mathrm{1}}}}}\:}\:{dx} \\ $$$$\: \\ $$

Question Number 156214 Answers: 0 Comments: 0

Question Number 156213 Answers: 0 Comments: 0

Ω =∫_0 ^1 log^2 (((Γ(x+1))/x)) dx = ?

$$\Omega\:=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\mathrm{log}^{\mathrm{2}} \:\left(\frac{\Gamma\left(\mathrm{x}+\mathrm{1}\right)}{\mathrm{x}}\right)\:\mathrm{dx}\:=\:? \\ $$

Question Number 156206 Answers: 1 Comments: 0

Ω :=∫_0 ^( 1) (√x) (√(1−(√x) )) (√(1−(√(1−(√x) )))) dx=?

$$ \\ $$$$\Omega\::=\int_{\mathrm{0}} ^{\:\mathrm{1}} \sqrt{{x}}\:\sqrt{\mathrm{1}−\sqrt{{x}}\:}\:\sqrt{\mathrm{1}−\sqrt{\mathrm{1}−\sqrt{{x}}\:}}\:{dx}=? \\ $$

Question Number 156205 Answers: 0 Comments: 0

Question Number 156194 Answers: 0 Comments: 1

∫_0 ^( 1) (√(x(√(x^2 (√(x^3 .....(√x^n ))))))) dx n ∈ N

$$\: \\ $$$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\sqrt{{x}\sqrt{{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{3}} .....\sqrt{{x}^{{n}} }}}}\:{dx} \\ $$$$\:\:\:\:\:\:\:\:\:{n}\:\in\:\mathbb{N} \\ $$$$\: \\ $$

Question Number 156180 Answers: 0 Comments: 0

Question Number 156334 Answers: 0 Comments: 1

Question Number 156178 Answers: 1 Comments: 0

Question Number 156177 Answers: 1 Comments: 0

∫_(−∞) ^∞ ((sin (x))/(x^2 +x+1))dx=?

$$\int_{−\infty} ^{\infty} \frac{\mathrm{sin}\:\left({x}\right)}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}{dx}=? \\ $$

Question Number 156176 Answers: 1 Comments: 0

Question Number 156172 Answers: 3 Comments: 6

Question Number 156170 Answers: 2 Comments: 0

Question Number 156164 Answers: 1 Comments: 0

Question Number 156182 Answers: 1 Comments: 0

Question Number 156152 Answers: 0 Comments: 1

{ ((a+b+c=1)),((a^2 +b^2 +c^2 =2)),((a^3 +b^3 +c^3 =3)) :} a^6 +b^6 +c^6 =?

$$\begin{cases}{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}}=\mathrm{1}}\\{\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{b}}^{\mathrm{2}} +\boldsymbol{\mathrm{c}}^{\mathrm{2}} =\mathrm{2}}\\{\boldsymbol{\mathrm{a}}^{\mathrm{3}} +\boldsymbol{\mathrm{b}}^{\mathrm{3}} +\boldsymbol{\mathrm{c}}^{\mathrm{3}} =\mathrm{3}}\end{cases} \\ $$$$\boldsymbol{\mathrm{a}}^{\mathrm{6}} +\boldsymbol{\mathrm{b}}^{\mathrm{6}} +\boldsymbol{\mathrm{c}}^{\mathrm{6}} =? \\ $$

Question Number 156138 Answers: 0 Comments: 1

la valeur de l′integrale ∫^1 _o x(√(√(√x)))

$${la}\:{valeur}\:{de}\:{l}'{integrale} \\ $$$$\underset{{o}} {\int}^{\mathrm{1}} {x}\sqrt{\sqrt{\sqrt{{x}}}} \\ $$$$ \\ $$

Question Number 156137 Answers: 1 Comments: 0

Question Number 156136 Answers: 1 Comments: 0

soit E(x) la partie entiere ,p<q alors la valeur de ∫^q _p E(x)dx =?

$${soit}\:{E}\left({x}\right)\:{la}\:{partie}\:{entiere}\:,{p}<{q} \\ $$$${alors}\:{la}\:{valeur}\:{de}\: \\ $$$$\underset{{p}} {\int}^{{q}} {E}\left({x}\right){dx}\:=? \\ $$

Question Number 156133 Answers: 1 Comments: 1

Question Number 156128 Answers: 1 Comments: 0

f:X→Y f(E\F)=f(E)\f(F)⇒f is 1 to 1 I think it is not true since let x1 x2 x3∈E ,x3 x4∈F, and f(x1)=f( x2) it will be not true. but my friend say by ∼q⇒∼p f is not 1 to 1 ⇒f(E\F)≠f(E)\f(F),and take x1 x2∈X, f(x1)=f(x2)=y0 E={x1 ,x2} F={x2} and can proof it is true but I do not know which is true how to proof it?

$$\:{f}:{X}\rightarrow{Y} \\ $$$${f}\left({E}\backslash{F}\right)={f}\left({E}\right)\backslash{f}\left({F}\right)\Rightarrow{f}\:{is}\:\mathrm{1}\:{to}\:\mathrm{1} \\ $$$$ \\ $$$${I}\:{think}\:{it}\:{is}\:{not}\:{true}\: \\ $$$${since}\:{let}\:{x}\mathrm{1}\:{x}\mathrm{2}\:{x}\mathrm{3}\in{E}\:,{x}\mathrm{3}\:{x}\mathrm{4}\in{F}, \\ $$$${and}\:{f}\left({x}\mathrm{1}\right)={f}\left(\:{x}\mathrm{2}\right)\:{it}\:{will}\:{be}\:{not}\:{true}. \\ $$$$ \\ $$$${but}\:{my}\:{friend}\:{say}\:{by}\:\sim{q}\Rightarrow\sim{p} \\ $$$$\:{f}\:{is}\:{not}\:\mathrm{1}\:{to}\:\mathrm{1} \\ $$$$\Rightarrow{f}\left({E}\backslash{F}\right)\neq{f}\left({E}\right)\backslash{f}\left({F}\right),{and}\:{take} \\ $$$${x}\mathrm{1}\:{x}\mathrm{2}\in{X},\:{f}\left({x}\mathrm{1}\right)={f}\left({x}\mathrm{2}\right)={y}\mathrm{0} \\ $$$${E}=\left\{{x}\mathrm{1}\:,{x}\mathrm{2}\right\}\:{F}=\left\{{x}\mathrm{2}\right\} \\ $$$${and}\:\:{can}\:{proof}\:{it}\:{is}\:{true} \\ $$$${but}\:{I}\:{do}\:{not}\:{know}\:{which}\:{is}\:{true} \\ $$$${how}\:{to}\:{proof}\:{it}? \\ $$

Question Number 156126 Answers: 1 Comments: 1

cos(π/5)=...? with solution pls

$$\:\:\:\mathrm{cos}\frac{\pi}{\mathrm{5}}=...?\:\:\mathrm{with}\:\mathrm{solution}\:\mathrm{pls} \\ $$

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