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Question-85059




Question Number 85059 by Power last updated on 18/Mar/20
Answered by MJS last updated on 18/Mar/20
x^5 +1=  =(x+1)(x^2 −((1−(√5))/2)x+1)(x^2 −((1+(√5))/2)x+1)  you′ll have to decompose and then use  formulas  c_2 ∫(dx/(x+c_1 ))  and  c_4 ∫((x+c_1 )/(x^2 +c_2 x+c_3 ))dx  you can find in any good formulary
$${x}^{\mathrm{5}} +\mathrm{1}= \\ $$$$=\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} −\frac{\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}}{x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} −\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}{x}+\mathrm{1}\right) \\ $$$$\mathrm{you}'\mathrm{ll}\:\mathrm{have}\:\mathrm{to}\:\mathrm{decompose}\:\mathrm{and}\:\mathrm{then}\:\mathrm{use} \\ $$$$\mathrm{formulas} \\ $$$${c}_{\mathrm{2}} \int\frac{{dx}}{{x}+{c}_{\mathrm{1}} } \\ $$$$\mathrm{and} \\ $$$${c}_{\mathrm{4}} \int\frac{{x}+{c}_{\mathrm{1}} }{{x}^{\mathrm{2}} +{c}_{\mathrm{2}} {x}+{c}_{\mathrm{3}} }{dx} \\ $$$$\mathrm{you}\:\mathrm{can}\:\mathrm{find}\:\mathrm{in}\:\mathrm{any}\:\mathrm{good}\:\mathrm{formulary} \\ $$
Commented by Power last updated on 19/Mar/20
step by step solution
$$\mathrm{step}\:\mathrm{by}\:\mathrm{step}\:\mathrm{solution} \\ $$
Commented by mr W last updated on 19/Mar/20
Power sir:  i think a little bit thing should be left  for you to do by yourself. you are not  our teacher and we are not your  students. that should be clear.  i think when someone brings  me food, i don′t request ihm to put  the food in my mouth. that should be  done by myself!  but when people give you hint for how  to solve a problem, you seem only  to know to ask for more. personally  i dislike this kind of behaviour.
$${Power}\:{sir}: \\ $$$${i}\:{think}\:{a}\:{little}\:{bit}\:{thing}\:{should}\:{be}\:{left} \\ $$$${for}\:{you}\:{to}\:{do}\:{by}\:{yourself}.\:{you}\:{are}\:{not} \\ $$$${our}\:{teacher}\:{and}\:{we}\:{are}\:{not}\:{your} \\ $$$${students}.\:{that}\:{should}\:{be}\:{clear}. \\ $$$${i}\:{think}\:{when}\:{someone}\:{brings} \\ $$$${me}\:{food},\:{i}\:{don}'{t}\:{request}\:{ihm}\:{to}\:{put} \\ $$$${the}\:{food}\:{in}\:{my}\:{mouth}.\:{that}\:{should}\:{be} \\ $$$${done}\:{by}\:{myself}! \\ $$$${but}\:{when}\:{people}\:{give}\:{you}\:{hint}\:{for}\:{how} \\ $$$${to}\:{solve}\:{a}\:{problem},\:{you}\:{seem}\:{only} \\ $$$${to}\:{know}\:{to}\:{ask}\:{for}\:{more}.\:{personally} \\ $$$${i}\:{dislike}\:{this}\:{kind}\:{of}\:{behaviour}. \\ $$

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