Find the antiderivative of : $frac{x^4}{left(x+1right)^2left(x^2+1right)}$












1














I'm trying to find the antiderivative of the following function:
$$frac{x^4}{left(x+1right)^2left(x^2+1right)}$$
Could you give me some tips as to how to proceed? Long division does not bring me very far, which is why I believe there must be a better way to go about this.
Thanks in advance for any input.






integration







share|cite|improve this question


















  • 1




    Partial fractions would be the standard approach -- do you know about them?
    – postmortes
    Nov 20 '18 at 10:21










  • Do you want an answer using long division?
    – Akash Roy
    Nov 20 '18 at 10:24










  • We cannot directly apply partial fractions, first we need to perform polynomial long division followed by application of linearity and then partial fractions @postmortes.
    – Akash Roy
    Nov 20 '18 at 10:25










  • @AkashRoy you might want to read lab bhattacharjee's answer :)
    – postmortes
    Nov 20 '18 at 10:35
















1














I'm trying to find the antiderivative of the following function:
$$frac{x^4}{left(x+1right)^2left(x^2+1right)}$$
Could you give me some tips as to how to proceed? Long division does not bring me very far, which is why I believe there must be a better way to go about this.
Thanks in advance for any input.






integration







share|cite|improve this question


















  • 1




    Partial fractions would be the standard approach -- do you know about them?
    – postmortes
    Nov 20 '18 at 10:21










  • Do you want an answer using long division?
    – Akash Roy
    Nov 20 '18 at 10:24










  • We cannot directly apply partial fractions, first we need to perform polynomial long division followed by application of linearity and then partial fractions @postmortes.
    – Akash Roy
    Nov 20 '18 at 10:25










  • @AkashRoy you might want to read lab bhattacharjee's answer :)
    – postmortes
    Nov 20 '18 at 10:35














1












1








1


1





I'm trying to find the antiderivative of the following function:
$$frac{x^4}{left(x+1right)^2left(x^2+1right)}$$
Could you give me some tips as to how to proceed? Long division does not bring me very far, which is why I believe there must be a better way to go about this.
Thanks in advance for any input.






integration







share|cite|improve this question













I'm trying to find the antiderivative of the following function:
$$frac{x^4}{left(x+1right)^2left(x^2+1right)}$$
Could you give me some tips as to how to proceed? Long division does not bring me very far, which is why I believe there must be a better way to go about this.
Thanks in advance for any input.






integration




integration






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share|cite|improve this question











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share|cite|improve this question










asked Nov 20 '18 at 10:19









DeltaXY

152




152








  • 1




    Partial fractions would be the standard approach -- do you know about them?
    – postmortes
    Nov 20 '18 at 10:21










  • Do you want an answer using long division?
    – Akash Roy
    Nov 20 '18 at 10:24










  • We cannot directly apply partial fractions, first we need to perform polynomial long division followed by application of linearity and then partial fractions @postmortes.
    – Akash Roy
    Nov 20 '18 at 10:25










  • @AkashRoy you might want to read lab bhattacharjee's answer :)
    – postmortes
    Nov 20 '18 at 10:35














  • 1




    Partial fractions would be the standard approach -- do you know about them?
    – postmortes
    Nov 20 '18 at 10:21










  • Do you want an answer using long division?
    – Akash Roy
    Nov 20 '18 at 10:24










  • We cannot directly apply partial fractions, first we need to perform polynomial long division followed by application of linearity and then partial fractions @postmortes.
    – Akash Roy
    Nov 20 '18 at 10:25










  • @AkashRoy you might want to read lab bhattacharjee's answer :)
    – postmortes
    Nov 20 '18 at 10:35








1




1




Partial fractions would be the standard approach -- do you know about them?
– postmortes
Nov 20 '18 at 10:21




Partial fractions would be the standard approach -- do you know about them?
– postmortes
Nov 20 '18 at 10:21












Do you want an answer using long division?
– Akash Roy
Nov 20 '18 at 10:24




Do you want an answer using long division?
– Akash Roy
Nov 20 '18 at 10:24












We cannot directly apply partial fractions, first we need to perform polynomial long division followed by application of linearity and then partial fractions @postmortes.
– Akash Roy
Nov 20 '18 at 10:25




We cannot directly apply partial fractions, first we need to perform polynomial long division followed by application of linearity and then partial fractions @postmortes.
– Akash Roy
Nov 20 '18 at 10:25












@AkashRoy you might want to read lab bhattacharjee's answer :)
– postmortes
Nov 20 '18 at 10:35




@AkashRoy you might want to read lab bhattacharjee's answer :)
– postmortes
Nov 20 '18 at 10:35










1 Answer
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3














Use Partial Fraction Decomposition,



$$frac{x^4}{left(x+1right)^2left(x^2+1right)}=1+dfrac A{x+1}+dfrac B{(x+1)^2}+dfrac{Cx+D}{x^2+1} $$



$1$ as the coefficient of the highest exponent of $x$ in numerator & that of the denominator are same.






share|cite|improve this answer





















  • Thank you very much.
    – DeltaXY
    Nov 20 '18 at 11:25











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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









3














Use Partial Fraction Decomposition,



$$frac{x^4}{left(x+1right)^2left(x^2+1right)}=1+dfrac A{x+1}+dfrac B{(x+1)^2}+dfrac{Cx+D}{x^2+1} $$



$1$ as the coefficient of the highest exponent of $x$ in numerator & that of the denominator are same.






share|cite|improve this answer





















  • Thank you very much.
    – DeltaXY
    Nov 20 '18 at 11:25
















3














Use Partial Fraction Decomposition,



$$frac{x^4}{left(x+1right)^2left(x^2+1right)}=1+dfrac A{x+1}+dfrac B{(x+1)^2}+dfrac{Cx+D}{x^2+1} $$



$1$ as the coefficient of the highest exponent of $x$ in numerator & that of the denominator are same.






share|cite|improve this answer





















  • Thank you very much.
    – DeltaXY
    Nov 20 '18 at 11:25














3












3








3






Use Partial Fraction Decomposition,



$$frac{x^4}{left(x+1right)^2left(x^2+1right)}=1+dfrac A{x+1}+dfrac B{(x+1)^2}+dfrac{Cx+D}{x^2+1} $$



$1$ as the coefficient of the highest exponent of $x$ in numerator & that of the denominator are same.






share|cite|improve this answer












Use Partial Fraction Decomposition,



$$frac{x^4}{left(x+1right)^2left(x^2+1right)}=1+dfrac A{x+1}+dfrac B{(x+1)^2}+dfrac{Cx+D}{x^2+1} $$



$1$ as the coefficient of the highest exponent of $x$ in numerator & that of the denominator are same.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Nov 20 '18 at 10:21









lab bhattacharjee

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  • Thank you very much.
    – DeltaXY
    Nov 20 '18 at 11:25


















  • Thank you very much.
    – DeltaXY
    Nov 20 '18 at 11:25
















Thank you very much.
– DeltaXY
Nov 20 '18 at 11:25




Thank you very much.
– DeltaXY
Nov 20 '18 at 11:25


















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