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let p(x)= (1+e^(iθ) x)^n −(1−e^(iθ) x)^n with n integr natural 1) find the roots of p(x) 2) fctorize inside C[x] p(x) 3) factorize inside R[x] p(x). θ ∈R

$${let}\:{p}\left({x}\right)=\:\left(\mathrm{1}+{e}^{{i}\theta} {x}\right)^{{n}} \:−\left(\mathrm{1}−{e}^{{i}\theta} {x}\right)^{{n}} \:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{fctorize}\:{inside}\:{C}\left[{x}\right]\:{p}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{factorize}\:{inside}\:{R}\left[{x}\right]\:{p}\left({x}\right).\:\:\theta\:\in{R} \\ $$

Question Number 39021 Answers: 0 Comments: 0

calculate A_n = ∫_0 ^1 sin(narctanx)dx with n integr natural. 2) find nature of Σ_n A_n

$${calculate}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{sin}\left({narctanx}\right){dx}\:\:{with}\:{n}\:{integr}\:{natural}. \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:\sum_{{n}} \:\:{A}_{{n}} \\ $$

Question Number 39020 Answers: 1 Comments: 0

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

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

Question Number 39019 Answers: 1 Comments: 3

calculate ∫ (dx/((x^2 +1)(x^2 +2)(x^2 +3))) 1) find the value of ∫_0 ^∞ (dx/((x^2 +1)(x^2 +2)(x^2 +3)))

$${calculate}\:\int\:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{2}\right)\left({x}^{\mathrm{2}} \:+\mathrm{3}\right)} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\mathrm{2}\right)\left({x}^{\mathrm{2}} \:+\mathrm{3}\right)} \\ $$

Question Number 39018 Answers: 0 Comments: 0

find nature of Σ_(n=0) ^∞ (((−1)^([x]) )/(2+cos(n[x])))

$${find}\:{nature}\:{of}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\:\frac{\left(−\mathrm{1}\right)^{\left[{x}\right]} }{\mathrm{2}+{cos}\left({n}\left[{x}\right]\right)} \\ $$

Question Number 39017 Answers: 0 Comments: 1

find ∫ ((−2x+3)/(x^2 ( x^3 +8)))dx 2) calculate ∫_1 ^(+∞) ((−2x+3)/(x^2 (x^3 +8)))dx

$${find}\:\:\:\int\:\:\frac{−\mathrm{2}{x}+\mathrm{3}}{{x}^{\mathrm{2}} \left(\:{x}^{\mathrm{3}} \:+\mathrm{8}\right)}{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{1}} ^{+\infty} \:\:\:\frac{−\mathrm{2}{x}+\mathrm{3}}{{x}^{\mathrm{2}} \left({x}^{\mathrm{3}} \:+\mathrm{8}\right)}{dx} \\ $$

Question Number 39016 Answers: 0 Comments: 0

calculate ∫_0 ^π ((sin(nx))/(cosx))dx with n from N .

$${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{sin}\left({nx}\right)}{{cosx}}{dx}\:\:{with}\:{n}\:{from}\:{N}\:. \\ $$

Question Number 39015 Answers: 0 Comments: 2

find ∫ (dx/(x(2x+1)(3x+2))) 2) calculate ∫_1 ^2 (dx/(x(2x+1)(3x+2)))

$${find}\:\:\int\:\:\:\:\:\:\frac{{dx}}{{x}\left(\mathrm{2}{x}+\mathrm{1}\right)\left(\mathrm{3}{x}+\mathrm{2}\right)} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\:\:\:\frac{{dx}}{{x}\left(\mathrm{2}{x}+\mathrm{1}\right)\left(\mathrm{3}{x}+\mathrm{2}\right)} \\ $$

Question Number 39013 Answers: 0 Comments: 1

Given the matrices A = ((3,5),(2,4) ) and I = ((1,0),(0,1) ) find matrix B if BA= I find A′ the reflection on the line y = x and A′′ the enlargement with matrix (((2 0)),((0 2)) ).

$${Given}\:{the}\:{matrices} \\ $$$${A}\:=\:\begin{pmatrix}{\mathrm{3}}&{\mathrm{5}}\\{\mathrm{2}}&{\mathrm{4}}\end{pmatrix}\:{and}\:{I}\:=\:\begin{pmatrix}{\mathrm{1}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{1}}\end{pmatrix} \\ $$$${find}\:{matrix}\:{B}\:{if}\: \\ $$$${BA}=\:{I} \\ $$$${find}\:{A}'\:{the}\:{reflection}\:{on}\:{the} \\ $$$${line}\:{y}\:=\:{x}\:{and}\:{A}''\:{the}\:{enlargement} \\ $$$${with}\:{matrix}\:\begin{pmatrix}{\mathrm{2}\:\:\:\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:\:\mathrm{2}}\end{pmatrix}. \\ $$

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