Mixing
Evaluating $int frac{x^n}{y}dx$ using reduction formula
$begingroup$
If $y^2=3x^2+2x+1$ and integration $I_n$ is defined as $I_n= int frac{x^n}{y}dx$, where $AI_{10}+BI_{9}+CI_{8}=x^9y$, then find the values of $A,B,C$.
I did generate the reduction formula but I am not getting any kind of given relation between the three integrations. I think my reduction formula approach is not good. How should I apply Integration by parts for reduction and how do I simplify after that. Thanks.
calculus integration reduction-formula
edited Jan 6 at 5:44
clathratus
3,740333
$endgroup$
add a comment |
$begingroup$
If $y^2=3x^2+2x+1$ and integration $I_n$ is defined as $I_n= int frac{x^n}{y}dx$, where $AI_{10}+BI_{9}+CI_{8}=x^9y$, then find the values of $A,B,C$.
I did generate the reduction formula but I am not getting any kind of given relation between the three integrations. I think my reduction formula approach is not good. How should I apply Integration by parts for reduction and how do I simplify after that. Thanks.
calculus integration reduction-formula
edited Jan 6 at 5:44
clathratus
3,740333
$endgroup$
add a comment |
$begingroup$
If $y^2=3x^2+2x+1$ and integration $I_n$ is defined as $I_n= int frac{x^n}{y}dx$, where $AI_{10}+BI_{9}+CI_{8}=x^9y$, then find the values of $A,B,C$.
I did generate the reduction formula but I am not getting any kind of given relation between the three integrations. I think my reduction formula approach is not good. How should I apply Integration by parts for reduction and how do I simplify after that. Thanks.
calculus integration reduction-formula
edited Jan 6 at 5:44
clathratus
3,740333
$endgroup$
If $y^2=3x^2+2x+1$ and integration $I_n$ is defined as $I_n= int frac{x^n}{y}dx$, where $AI_{10}+BI_{9}+CI_{8}=x^9y$, then find the values of $A,B,C$.
I did generate the reduction formula but I am not getting any kind of given relation between the three integrations. I think my reduction formula approach is not good. How should I apply Integration by parts for reduction and how do I simplify after that. Thanks.
calculus integration reduction-formula
calculus integration reduction-formula
edited Jan 6 at 5:44
clathratus
3,740333
edited Jan 6 at 5:44
clathratus
3,740333
edited Jan 6 at 5:44
clathratus
3,740333
edited Jan 6 at 5:44
clathratus
3,740333
edited Jan 6 at 5:44
clathratus
3,740333
3,740333
asked May 16 '16 at 13:46
user167045
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1 Answer
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$begingroup$
$(x^n y)'=n x^{n-1}y+x^n y'$ with $y=frac{3x^2+2x+1}{y}$ and $y'=frac{3x+1}{y}$.
$I_n'=frac{x^n}{y}$
=> $Afrac{x^{10}}{y}+Bfrac{x^9}{y}+Cfrac{x^8}{y}=
9 x^8frac{3x^2+2x+1}{y}+x^9 frac{3x+1}{y}$
Compare the coefficients of $frac{x^8}{y}$, $frac{x^9}{y}$ and $frac{x^{10}}{y}$.
answered May 16 '16 at 15:50
user90369user90369
8,158925
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1 Answer
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$begingroup$
$(x^n y)'=n x^{n-1}y+x^n y'$ with $y=frac{3x^2+2x+1}{y}$ and $y'=frac{3x+1}{y}$.
$I_n'=frac{x^n}{y}$
=> $Afrac{x^{10}}{y}+Bfrac{x^9}{y}+Cfrac{x^8}{y}=
9 x^8frac{3x^2+2x+1}{y}+x^9 frac{3x+1}{y}$
Compare the coefficients of $frac{x^8}{y}$, $frac{x^9}{y}$ and $frac{x^{10}}{y}$.
answered May 16 '16 at 15:50
user90369user90369
8,158925
$endgroup$
add a comment |
$begingroup$
$(x^n y)'=n x^{n-1}y+x^n y'$ with $y=frac{3x^2+2x+1}{y}$ and $y'=frac{3x+1}{y}$.
$I_n'=frac{x^n}{y}$
=> $Afrac{x^{10}}{y}+Bfrac{x^9}{y}+Cfrac{x^8}{y}=
9 x^8frac{3x^2+2x+1}{y}+x^9 frac{3x+1}{y}$
Compare the coefficients of $frac{x^8}{y}$, $frac{x^9}{y}$ and $frac{x^{10}}{y}$.
answered May 16 '16 at 15:50
user90369user90369
8,158925
$endgroup$
add a comment |
$begingroup$
$(x^n y)'=n x^{n-1}y+x^n y'$ with $y=frac{3x^2+2x+1}{y}$ and $y'=frac{3x+1}{y}$.
$I_n'=frac{x^n}{y}$
=> $Afrac{x^{10}}{y}+Bfrac{x^9}{y}+Cfrac{x^8}{y}=
9 x^8frac{3x^2+2x+1}{y}+x^9 frac{3x+1}{y}$
Compare the coefficients of $frac{x^8}{y}$, $frac{x^9}{y}$ and $frac{x^{10}}{y}$.
answered May 16 '16 at 15:50
user90369user90369
8,158925
$endgroup$
$(x^n y)'=n x^{n-1}y+x^n y'$ with $y=frac{3x^2+2x+1}{y}$ and $y'=frac{3x+1}{y}$.
$I_n'=frac{x^n}{y}$
=> $Afrac{x^{10}}{y}+Bfrac{x^9}{y}+Cfrac{x^8}{y}=
9 x^8frac{3x^2+2x+1}{y}+x^9 frac{3x+1}{y}$
Compare the coefficients of $frac{x^8}{y}$, $frac{x^9}{y}$ and $frac{x^{10}}{y}$.
answered May 16 '16 at 15:50
user90369user90369
8,158925
answered May 16 '16 at 15:50
user90369user90369
8,158925
answered May 16 '16 at 15:50
user90369user90369
8,158925
answered May 16 '16 at 15:50
user90369user90369
8,158925
8,158925
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