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find-4-dx-x-1-3-x-3-5-




Question Number 208062 by mathzup last updated on 03/Jun/24
find  ∫_4 ^∞     (dx/((x+1)^3 (x−3)^5 ))
find4dx(x+1)3(x3)5
Answered by Frix last updated on 03/Jun/24
Use Ostrogradski′s Method (search it on  the www)  ∫(dx/((x+1)^3 (x−3)^5 ))=((15)/(4096))∫(dx/((x+1)(x+3)))+  +((15x^5 −135x^4 +350x^3 +10x^2 −877x+125)/(4096(x+1)^2 (x−3)^4 ))=  =((15ln ∣((x−3)/(x+1))∣)/(16384))+((15x^5 −135x^4 +350x^3 +10x^2 −877x+125)/(4096(x+1)^2 (x−3)^4 ))+C  ⇒  Answer is ((23)/(102400))+((15ln 5)/(16374))
UseOstrogradskisMethod(searchitonthewww)dx(x+1)3(x3)5=154096dx(x+1)(x+3)++15x5135x4+350x3+10x2877x+1254096(x+1)2(x3)4==15lnx3x+116384+15x5135x4+350x3+10x2877x+1254096(x+1)2(x3)4+CAnsweris23102400+15ln516374

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