Mixing
Find the antiderivative of : $frac{x^4}{left(x+1right)^2left(x^2+1right)}$
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
asked Nov 20 '18 at 10:19
DeltaXY
152
add a comment |
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
asked Nov 20 '18 at 10:19
DeltaXY
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
add a comment |
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
asked Nov 20 '18 at 10:19
DeltaXY
152
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
asked Nov 20 '18 at 10:19
DeltaXY
152
asked Nov 20 '18 at 10:19
DeltaXY
152
asked Nov 20 '18 at 10:19
DeltaXY
152
asked Nov 20 '18 at 10:19
DeltaXY
152
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
add a comment |
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
add a comment |
1 Answer
1
active
oldest
votes
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.
answered Nov 20 '18 at 10:21
lab bhattacharjee
223k15156274
Thank you very much.
– DeltaXY
Nov 20 '18 at 11:25
add a comment |
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1 Answer
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active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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.
answered Nov 20 '18 at 10:21
lab bhattacharjee
223k15156274
Thank you very much.
– DeltaXY
Nov 20 '18 at 11:25
add a comment |
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.
answered Nov 20 '18 at 10:21
lab bhattacharjee
223k15156274
Thank you very much.
– DeltaXY
Nov 20 '18 at 11:25
add a comment |
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.
answered Nov 20 '18 at 10:21
lab bhattacharjee
223k15156274
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.
answered Nov 20 '18 at 10:21
lab bhattacharjee
223k15156274
answered Nov 20 '18 at 10:21
lab bhattacharjee
223k15156274
answered Nov 20 '18 at 10:21
lab bhattacharjee
223k15156274
answered Nov 20 '18 at 10:21
lab bhattacharjee
223k15156274
223k15156274
Thank you very much.
– DeltaXY
Nov 20 '18 at 11:25
add a comment |
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
add a comment |
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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