Question and Answers Forum

AllQuestion and Answers: Page 1153

Question Number 99120 Answers: 0 Comments: 2

prove that: ∫_(−(1/2)) ^∞ e^(−(4x^6 +12x^5 +15x^4 +10x^3 +4x^2 +x)) dx =((e)^(1/8) /3)[((Γ((1/6))^((−1)/2) )/(2(2)^(1/3) ))1F2(_(1/3,2/3) ^(1/6) ∣((−1)/(69/2)) ) +((Γ(5/6))/(128(4)^(1/3) ))1F2(_(4/3,5/3) ^(5/6) ∣((−1)/(69/2))) −((√π)/(16))12(_(2/3,4/3) ^(1/2) ∣((−1)/(69/2)))

$${prove}\:{that}: \\ $$$$\int_{−\frac{\mathrm{1}}{\mathrm{2}}} ^{\infty} {e}^{−\left(\mathrm{4}{x}^{\mathrm{6}} +\mathrm{12}{x}^{\mathrm{5}} +\mathrm{15}{x}^{\mathrm{4}} +\mathrm{10}{x}^{\mathrm{3}} +\mathrm{4}{x}^{\mathrm{2}} +{x}\right)} {dx} \\ $$$$=\frac{\sqrt[{\mathrm{8}}]{{e}}}{\mathrm{3}}\left[\frac{\Gamma\left(\frac{\mathrm{1}}{\mathrm{6}}\right)^{\frac{−\mathrm{1}}{\mathrm{2}}} }{\mathrm{2}\sqrt[{\mathrm{3}}]{\mathrm{2}}}\mathrm{1}{F}\mathrm{2}\left(_{\mathrm{1}/\mathrm{3},\mathrm{2}/\mathrm{3}} ^{\mathrm{1}/\mathrm{6}} \mid\frac{−\mathrm{1}}{\mathrm{69}/\mathrm{2}}\:\right)\:+\frac{\Gamma\left(\mathrm{5}/\mathrm{6}\right)}{\mathrm{128}\sqrt[{\mathrm{3}}]{\mathrm{4}}}\mathrm{1}{F}\mathrm{2}\left(_{\mathrm{4}/\mathrm{3},\mathrm{5}/\mathrm{3}} ^{\mathrm{5}/\mathrm{6}} \mid\frac{−\mathrm{1}}{\mathrm{69}/\mathrm{2}}\right)\:−\frac{\sqrt{\pi}}{\mathrm{16}}\mathrm{12}\left(_{\mathrm{2}/\mathrm{3},\mathrm{4}/\mathrm{3}} ^{\mathrm{1}/\mathrm{2}} \mid\frac{−\mathrm{1}}{\mathrm{69}/\mathrm{2}}\right)\:\right. \\ $$

Question Number 99118 Answers: 4 Comments: 0

Question Number 99117 Answers: 1 Comments: 0

let a,b,c ∈R determine the minimum value ((3a)/(b+c))+((4b)/(a+c))+((5c)/(a+b))

$${let}\:{a},{b},{c}\:\in\mathbb{R}\:{determine}\:{the}\:{minimum} \\ $$$${value} \\ $$$$ \\ $$$$\frac{\mathrm{3}{a}}{{b}+{c}}+\frac{\mathrm{4}{b}}{{a}+{c}}+\frac{\mathrm{5}{c}}{{a}+{b}} \\ $$

Question Number 99114 Answers: 1 Comments: 0

calculate: ∫(√x)sinh^(−1) (x)dx where sinh^(−1) (x) is the inverse hyperbolic sine function

$${calculate}: \\ $$$$\int\sqrt{{x}}{sinh}^{−\mathrm{1}} \left({x}\right){dx} \\ $$$${where}\:{sinh}^{−\mathrm{1}} \left({x}\right)\:{is}\:{the}\:{inverse}\:{hyperbolic}\: \\ $$$${sine}\:{function} \\ $$$$ \\ $$$$ \\ $$

Question Number 99113 Answers: 2 Comments: 0

solve y^(′′) +5y^′ −3y =x^2 sin(3x) with y(0) =0 and y^′ (0)=−1

$$\mathrm{solve}\:\mathrm{y}^{''} \:+\mathrm{5y}^{'} \:−\mathrm{3y}\:=\mathrm{x}^{\mathrm{2}} \:\mathrm{sin}\left(\mathrm{3x}\right)\:\:\mathrm{with}\:\mathrm{y}\left(\mathrm{0}\right)\:=\mathrm{0}\:\mathrm{and}\:\mathrm{y}^{'} \left(\mathrm{0}\right)=−\mathrm{1} \\ $$

Question Number 99102 Answers: 0 Comments: 21

Question Number 99097 Answers: 0 Comments: 1

Hello verry nice day for all of you god bless You pleas Can you use black Color shen You post Quation or Give answer is verry hard to read withe other colors

$${Hello}\: \\ $$$${verry}\:{nice}\:{day}\:{for}\:{all}\:{of}\:{you}\:{god}\:{bless}\:{You} \\ $$$${pleas}\:{Can}\:{you}\:{use}\:{black}\:{Color}\:{shen}\:{You}\:{post}\:{Quation}\: \\ $$$${or}\:{Give}\:{answer}\:{is}\:{verry}\:{hard}\:{to}\:{read}\:{withe}\:{other}\:{colors} \\ $$

Question Number 99095 Answers: 1 Comments: 0