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Question Number 156295 Answers: 2 Comments: 0

Question Number 156292 Answers: 0 Comments: 0

(1/3)+(3/(3×7))+(5/(3×7×11))+(7/(3×7×11×15))+…

$$\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{3}}{\mathrm{3}×\mathrm{7}}+\frac{\mathrm{5}}{\mathrm{3}×\mathrm{7}×\mathrm{11}}+\frac{\mathrm{7}}{\mathrm{3}×\mathrm{7}×\mathrm{11}×\mathrm{15}}+\ldots \\ $$

Question Number 156290 Answers: 0 Comments: 0

Question Number 156281 Answers: 2 Comments: 0

∫_(−3) ^5 (√(∣x∣^3 ))dx

$$\int_{−\mathrm{3}} ^{\mathrm{5}} \:\sqrt{\mid{x}\mid^{\mathrm{3}} }{dx} \\ $$

Question Number 156275 Answers: 1 Comments: 0

Helllo to All Good (morning night) we are her too shar our knowelegdes we must respect evrey one we need that positiv energy sorry for my English

$${Helllo}\:{to}\:{All}\:{Good}\:\left({morning}\:{night}\right) \\ $$$${we}\:{are}\:{her}\:{too}\:{shar}\:{our}\:{knowelegdes} \\ $$$${we}\:{must}\:{respect}\:{evrey}\:{one}\:{we}\:{need}\:{that} \\ $$$${positiv}\:{energy}\:{sorry}\:{for}\:{my}\:{English} \\ $$$$ \\ $$

Question Number 156270 Answers: 1 Comments: 1

Show that i = sin^(− 1) (((√2)/2))^2 in air, if the refractive index n = ((sin^2 (60))/(sin^2 (45)))

$$\mathrm{Show}\:\mathrm{that}\:\:\:\:\:\:\mathrm{i}\:\:\:\:=\:\:\:\mathrm{sin}^{−\:\mathrm{1}} \left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\right)^{\mathrm{2}} \:\:\:\:\mathrm{in}\:\mathrm{air},\:\mathrm{if}\:\mathrm{the}\:\mathrm{refractive} \\ $$$$\mathrm{index}\:\:\:\:\:\:\:\:\mathrm{n}\:\:\:=\:\:\:\frac{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{60}\right)}{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{45}\right)} \\ $$

Question Number 156259 Answers: 0 Comments: 0

Question Number 156257 Answers: 0 Comments: 0

∫ ((xsin^(−1) (x^2 ))/(1−x^4 )) dx=?

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

Question Number 156253 Answers: 1 Comments: 0

Question Number 156252 Answers: 1 Comments: 1

Question Number 156250 Answers: 0 Comments: 1

lim_(x→0) ((1−cos x (√(cos 2x)) ((cos 3x))^(1/3) ((cos 4x))^(1/4) )/x^2 ) =?

$$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{x}\:\sqrt{\mathrm{cos}\:\mathrm{2x}}\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{3x}}\:\sqrt[{\mathrm{4}}]{\mathrm{cos}\:\mathrm{4x}}}{\mathrm{x}^{\mathrm{2}} }\:=? \\ $$

Question Number 156248 Answers: 1 Comments: 0

Question Number 156244 Answers: 1 Comments: 0

solve the pairs of simultaneous equations ax−2y=2 x+3y=3 qy−px=(q^2 −p^2 )/pq py+qx=2

$${solve}\:{the}\:{pairs}\:{of}\:{simultaneous}\:{equations} \\ $$$${ax}−\mathrm{2}{y}=\mathrm{2} \\ $$$${x}+\mathrm{3}{y}=\mathrm{3} \\ $$$${qy}−{px}=\left({q}^{\mathrm{2}} −{p}^{\mathrm{2}} \right)/{pq} \\ $$$${py}+{qx}=\mathrm{2} \\ $$

Question Number 156240 Answers: 0 Comments: 3

∫^(π/2) _((−π)/2) ∣sin(x)∣ dx ∫^π _0 ∣cos(x)∣dx

$$\underset{\frac{−\pi}{\mathrm{2}}} {\int}^{\frac{\pi}{\mathrm{2}}} \mid{sin}\left({x}\right)\mid\:{dx} \\ $$$$\underset{\mathrm{0}} {\int}^{\pi} \mid{cos}\left({x}\right)\mid{dx} \\ $$

Question Number 156269 Answers: 0 Comments: 1

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

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