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Question Number 60682 Answers: 0 Comments: 1

simplify S_n =Σ_(k=0) ^n sin^k (x)cos(kx)

$${simplify}\:\:\:\:{S}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\:{sin}^{{k}} \left({x}\right){cos}\left({kx}\right)\:\:\: \\ $$

Question Number 60681 Answers: 0 Comments: 1

calculate L(e^(−2x) sin(αx)) α real and L laplace transform

$${calculate}\:\:{L}\left({e}^{−\mathrm{2}{x}} {sin}\left(\alpha{x}\right)\right)\:\:\:\:\alpha\:{real}\:\:\:{and}\:{L}\:{laplace}\:{transform} \\ $$

Question Number 60680 Answers: 0 Comments: 2

study the integral ∫_0 ^1 (x/(ln(1−x)))dx

$${study}\:{the}\:{integral}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{x}}{{ln}\left(\mathrm{1}−{x}\right)}{dx} \\ $$

Question Number 60679 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((ln(1+e^(−x^2 ) ))/(x^2 +4)) dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left(\mathrm{1}+{e}^{−{x}^{\mathrm{2}} } \right)}{{x}^{\mathrm{2}} \:+\mathrm{4}}\:{dx} \\ $$

Question Number 60678 Answers: 0 Comments: 3

calculate ∫_0 ^1 ((ln(1−x^2 ))/x) dx

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

Question Number 60677 Answers: 0 Comments: 0

let S_n =Σ_(k=1) ^n sin(((k^2 π)/n^3 )) determine lim_(n→∞) S_n

$${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:{sin}\left(\frac{{k}^{\mathrm{2}} \pi}{{n}^{\mathrm{3}} }\right)\:\:{determine}\:{lim}_{{n}\rightarrow\infty} \:\:{S}_{{n}} \\ $$

Question Number 60676 Answers: 1 Comments: 2

let S_n =Σ_(k=1) ^n sin^2 (((kπ)/n^2 )) find lim_(n→∞) S_n

$${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\:{sin}^{\mathrm{2}} \left(\frac{{k}\pi}{{n}^{\mathrm{2}} }\right)\:\:\:\:\:{find}\:{lim}_{{n}\rightarrow\infty} \:\:{S}_{{n}} \\ $$

Question Number 60670 Answers: 1 Comments: 2

Question Number 60808 Answers: 1 Comments: 8

Prove or disprove that there is a positive integer suitable for n^3 + 1 ∣ n! ( n! is divided by n^3 + 1 ) n ∈ Z^+

$${Prove}\:\:{or}\:\:{disprove}\:\:{that}\:\:{there}\:\:{is} \\ $$$${a}\:\:{positive}\:\:{integer}\:\:{suitable}\:\:{for} \\ $$$$\:\:\:\:\:\:\:{n}^{\mathrm{3}} \:+\:\mathrm{1}\:\:\:\mid\:\:\:{n}!\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\:\:{n}!\:\:\:{is}\:\:{divided}\:\:{by}\:\:{n}^{\mathrm{3}} \:+\:\mathrm{1}\:\:\right) \\ $$$${n}\:\:\in\:\:\mathbb{Z}^{+} \\ $$

Question Number 60675 Answers: 0 Comments: 0

∫_0 ^(π/2) ln[((ln^2 (sin(x)))/(π^2 +ln^2 (sinx)))]((ln(cos(x)))/(tan(x)))dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left[\frac{{ln}^{\mathrm{2}} \left({sin}\left({x}\right)\right)}{\pi^{\mathrm{2}} +{ln}^{\mathrm{2}} \left({sinx}\right)}\right]\frac{{ln}\left({cos}\left({x}\right)\right)}{{tan}\left({x}\right)}{dx} \\ $$

Question Number 60662 Answers: 0 Comments: 0

Question Number 60659 Answers: 1 Comments: 1

find ∫_0 ^1 ln(x)ln(1−x^2 )dx

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\right){ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 60658 Answers: 0 Comments: 1

calculate ∫_0 ^1 ln(x)ln(1−x)ln(1−x^2 )dx

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

Question Number 60644 Answers: 0 Comments: 0

Question Number 60637 Answers: 1 Comments: 1

Question Number 60636 Answers: 1 Comments: 0

Number of different permutation of MISSISSIPI is ...

$${Number}\:\:{of}\:\:{different}\:\:{permutation}\:\:{of}\:\:\:{MISSISSIPI}\:\:\:{is}\:\:... \\ $$

Question Number 60635 Answers: 2 Comments: 0

Question Number 60647 Answers: 0 Comments: 3

Question Number 60628 Answers: 0 Comments: 0

Who know dynamics about?

$${Who}\:\:{know}\:{dynamics}\:{about}? \\ $$

Question Number 60620 Answers: 3 Comments: 0

4^x + 9^x + 25^x = 6^x + 10^x + 15^x x = ?

$$\mathrm{4}^{{x}} \:+\:\mathrm{9}^{{x}} \:+\:\mathrm{25}^{{x}} \:\:=\:\:\mathrm{6}^{{x}} \:+\:\mathrm{10}^{{x}} \:+\:\mathrm{15}^{{x}} \\ $$$${x}\:\:=\:\:? \\ $$

Question Number 60623 Answers: 0 Comments: 0

What are all intregal methods that exist like trigonometry sub. Gaussian method feyman method ?

$$\mathrm{W}{hat}\:{are}\:{all}\:{intregal}\:{methods}\:{that}\:{exist} \\ $$$${like}\:{trigonometry}\:{sub}.\:{Gaussian}\:{method}\:{feyman}\:{method}\:? \\ $$$$ \\ $$$$ \\ $$

Question Number 60621 Answers: 0 Comments: 5

if π is rational then there exists a I_n =(v^(2n) /(n!))∫_0 ^π x^n (x−π)^n sin(x)dx can someone give a easier way to expaned this

$${if}\:\pi\:{is}\:{rational}\:{then}\:{there} \\ $$$${exists}\:{a}\:{I}_{{n}} =\frac{{v}^{\mathrm{2}{n}} }{{n}!}\underset{\mathrm{0}} {\overset{\pi} {\int}}{x}^{{n}} \left({x}−\pi\right)^{{n}} {sin}\left({x}\right){dx} \\ $$$${can}\:{someone}\:{give}\:{a}\:{easier}\:{way}\:{to}\:{expaned}\:{this} \\ $$

Question Number 60631 Answers: 0 Comments: 0

prove that∫_(−∞) ^∞ x^5 e^(−x^2 ) sin(x^3 ) dx=0.25474

$$\mathrm{prove}\:\mathrm{that}\underset{−\infty} {\overset{\infty} {\int}}\mathrm{x}^{\mathrm{5}} \mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{sin}\left(\mathrm{x}^{\mathrm{3}} \right)\:\mathrm{dx}=\mathrm{0}.\mathrm{25474} \\ $$

Question Number 60611 Answers: 1 Comments: 0

prove that ∫_(−∞) ^∞ x^2 e^(−x^2 ) cos(x^2 )sin(x^2 ) dx = (((√π)sin((3/2)tan^(−1) (2)))/(4 ((125))^(1/4) )) anyone can help me with this please

$${prove}\:{that}\:\underset{−\infty} {\overset{\infty} {\int}}{x}^{\mathrm{2}} {e}^{−{x}^{\mathrm{2}} } {cos}\left({x}^{\mathrm{2}} \right){sin}\left({x}^{\mathrm{2}} \right)\:{dx}\:=\:\frac{\sqrt{\pi}{sin}\left(\frac{\mathrm{3}}{\mathrm{2}}{tan}^{−\mathrm{1}} \left(\mathrm{2}\right)\right)}{\mathrm{4}\:\sqrt[{\mathrm{4}}]{\mathrm{125}}} \\ $$$${anyone}\:{can}\:{help}\:{me}\:{with}\:{this}\:{please} \\ $$$$ \\ $$

Question Number 60597 Answers: 0 Comments: 3

Question Number 60588 Answers: 0 Comments: 1

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