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Question Number 215504 Answers: 1 Comments: 0

simplify a−{b^(c−b) +⟨(b^(c−b) )^2 +((a/2))^2 ⟩+(a/2)}+c^(ab−c) −c^(a−c)

$$\mathrm{simplify}\:{a}−\left\{{b}^{{c}−{b}} +\langle\left({b}^{{c}−{b}} \right)^{\mathrm{2}} +\left(\frac{{a}}{\mathrm{2}}\right)^{\mathrm{2}} \rangle+\frac{{a}}{\mathrm{2}}\right\}+{c}^{{ab}−{c}} −{c}^{{a}−{c}} \\ $$

Question Number 215527 Answers: 1 Comments: 0

t_(33) ′ab+t_(00) ′ab=? Clearing up defintions: t_(33) ′a=(a−(√(36)))×3 t_(00) ′a=(a−(√(36)))×0 t′a=a−(√(36)) t′a= “transformation” of a

$${t}_{\mathrm{33}} '{ab}+{t}_{\mathrm{00}} '{ab}=? \\ $$$$ \\ $$$$\mathrm{Clearing}\:\mathrm{up}\:\mathrm{defintions}: \\ $$$${t}_{\mathrm{33}} '{a}=\left({a}−\sqrt{\mathrm{36}}\right)×\mathrm{3} \\ $$$${t}_{\mathrm{00}} '{a}=\left({a}−\sqrt{\mathrm{36}}\right)×\mathrm{0} \\ $$$${t}'{a}={a}−\sqrt{\mathrm{36}} \\ $$$${t}'{a}=\:``\mathrm{transformation}''\:\mathrm{of}\:{a} \\ $$

Question Number 215498 Answers: 2 Comments: 0

∫(e^(−ωu) +cos(u)−((sin(ωu))/e^u ))du

$$\int\left({e}^{−\omega{u}} +\mathrm{cos}\left({u}\right)−\frac{\mathrm{sin}\left(\omega{u}\right)}{{e}^{{u}} }\right){du} \\ $$

Question Number 215496 Answers: 1 Comments: 1

∫_0 ^π ((xtanx)/(secx + tanx)) dx Solve the integral.

$$\int_{\mathrm{0}} ^{\pi} \frac{{x}\mathrm{tan}{x}}{\mathrm{sec}{x}\:+\:\mathrm{tan}{x}}\:{dx} \\ $$$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{integral}. \\ $$

Question Number 215515 Answers: 0 Comments: 0

Question Number 215516 Answers: 1 Comments: 0

prove: Σ_(n=1) ^∞ (1/(π^2 n^2 +1))=(1/(e^2 −1))

$$\:\:\:\:\:\:\mathrm{prove}: \\ $$$$\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\pi^{\mathrm{2}} {n}^{\mathrm{2}} +\mathrm{1}}=\frac{\mathrm{1}}{{e}^{\mathrm{2}} −\mathrm{1}} \\ $$

Question Number 215492 Answers: 1 Comments: 1

Question Number 215572 Answers: 0 Comments: 1

Question Number 215473 Answers: 1 Comments: 0

Solve for x 2sin^2 x+3sin(x)+1=0 for 0 ≤ x

$${Solve}\:{for}\:{x} \\ $$$$ \\ $$$$\mathrm{2}{sin}^{\mathrm{2}} {x}+\mathrm{3}{sin}\left({x}\right)+\mathrm{1}=\mathrm{0}\:{for}\:\mathrm{0}\:\leqslant\:{x} \\ $$

Question Number 215528 Answers: 0 Comments: 2

Question Number 215469 Answers: 2 Comments: 0

Question Number 215468 Answers: 2 Comments: 0

((∂xω)/(∂yω))∙(∂e/∂ω)=? x=f(y) ω=g(y) e=h(ω)

$$\frac{\partial{x}\omega}{\partial{y}\omega}\centerdot\frac{\partial{e}}{\partial\omega}=? \\ $$$${x}={f}\left({y}\right) \\ $$$$\omega={g}\left({y}\right) \\ $$$${e}={h}\left(\omega\right) \\ $$

Question Number 215467 Answers: 0 Comments: 0

Question Number 215454 Answers: 1 Comments: 0

Question Number 215439 Answers: 2 Comments: 0

( 2 + (√2) )^8 = (√A) + (√B) Find: A−B = ?

$$\left(\:\mathrm{2}\:\:+\:\:\sqrt{\mathrm{2}}\:\right)^{\mathrm{8}} \:=\:\:\sqrt{\mathrm{A}}\:\:+\:\:\sqrt{\mathrm{B}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{A}−\mathrm{B}\:=\:? \\ $$

Question Number 215434 Answers: 0 Comments: 0

∫_0 ^( t) (√(t/(b−t))) e^t dt =?

$$\int_{\mathrm{0}} ^{\:\:{t}} \sqrt{\frac{{t}}{{b}−{t}}}\:{e}^{{t}} {dt}\:=? \\ $$

Question Number 215458 Answers: 1 Comments: 0

Evaluate lim_(n→∞) n^2 ∫_0 ^1 x^(n+1) sin(πx)dx

$$\mathrm{Evaluate}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{n}^{\mathrm{2}} \:\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}+\mathrm{1}} \mathrm{sin}\left(\pi{x}\right){dx} \\ $$

Question Number 215418 Answers: 1 Comments: 0

Question Number 215417 Answers: 1 Comments: 0

a and b are complex numbers such that ∣b∣ = 1. Find ∣((b − a)/(1 − a^(−) b))∣

$${a}\:\mathrm{and}\:{b}\:\mathrm{are}\:\mathrm{complex}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mid{b}\mid\:=\:\mathrm{1}.\:\mathrm{Find}\:\mid\frac{{b}\:−\:{a}}{\mathrm{1}\:−\:\overline {{a}b}}\mid \\ $$

Question Number 215414 Answers: 1 Comments: 2

∫ ((sin^3 ((x/2))sec((x/2)))/( (√(cos^3 x + cos^2 x + cosx)))) dx Solve this integral.

$$\int\:\frac{\mathrm{sin}^{\mathrm{3}} \left(\frac{{x}}{\mathrm{2}}\right)\mathrm{sec}\left(\frac{{x}}{\mathrm{2}}\right)}{\:\sqrt{\mathrm{cos}^{\mathrm{3}} {x}\:+\:\mathrm{cos}^{\mathrm{2}} {x}\:+\:\mathrm{cos}{x}}}\:{dx} \\ $$$$\mathrm{Solve}\:\mathrm{this}\:\mathrm{integral}. \\ $$

Question Number 215445 Answers: 3 Comments: 0

Question Number 215404 Answers: 1 Comments: 0

∫_a ^( x) ((√(1+4x^2 ))/( (√(a^2 −x^2 ))))dx = ?

$$\int_{{a}} ^{\:\:{x}} \:\frac{\sqrt{\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} }}{\:\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }}{dx}\:=\:? \\ $$

Question Number 215400 Answers: 3 Comments: 1

Question Number 215393 Answers: 0 Comments: 1

∫_0 ^∞ (x^(2ν) /((x^2 +β^2 )^(μ+1) ))sin(ax)dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{2}\nu} }{\left({x}^{\mathrm{2}} +\beta^{\mathrm{2}} \right)^{\mu+\mathrm{1}} }\mathrm{sin}\left({ax}\right){dx} \\ $$$$ \\ $$

Question Number 215386 Answers: 1 Comments: 0

Question Number 215372 Answers: 1 Comments: 0

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