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Question Number 211879 by Spillover last updated on 23/Sep/24

Answered by BHOOPENDRA last updated on 23/Sep/24

= (((x−4))/(10(x^2 −4x+5))) +(1/(10))∫ ((x−4)/(x^3 −4x^2 +5x)) (by ostrogradsky′s method) =((x−4)/(10(x^2 −4x+5)))+(1/(10))[∫((4x−11)/(5(x^2 −4x+5)))dx−∫(4/(5x)) dx] =((x−4)/(10(x^2 −4x+5)))+((−4ln(∣x∣)+2ln(x^2 −4x+5)−3tan^(−1) (x−2))/(50))+c

=(x−4)10(x2−4x+5)+110∫x−4x3−4x2+5x(byostrogradsky′smethod)=x−410(x2−4x+5)+110[∫4x−115(x2−4x+5)dx−∫45xdx]=x−410(x2−4x+5)+−4ln(∣x∣)+2ln(x2−4x+5)−3tan−1(x−2)50+c

Commented by Spillover last updated on 23/Sep/24

correct.thanks

correct.thanks

Answered by Spillover last updated on 23/Sep/24

Answered by Spillover last updated on 23/Sep/24

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