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tylersmith7690
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Integral help!
Evaluate the following inde nite integral,
∫[itex]\frac{x^3-5x}{x^3-2x^2+4x-8}[/itex] dx
I think I am right until i get to equating the equations when I do it the method I am taught in class I get c=0 and I don't think that is right. However when i put it into a system of equations with the coefficients i get fractions.
I would like to know what to do next. Thanks
First the degree of numerator is same as the denomenator. So i do long division and end up with
∫1+ [itex]\frac{2x^2-9x+8}{x^3-2x^2+4x-8}[/itex]
Now decompose the fraction part into:
[itex]\frac{2x^2-9x+8}{(x^2+4)(x-2)}[/itex] =[itex]\frac{Ax+B}{(x^2+4)}[/itex]+[itex]\frac{C}{(x-2)}[/itex]
Then get a common denomenator for RHS
= [itex]\frac{(Ax+B)(x-2)+C(x^2+4)}{(x^2+4)(x-2)}[/itex]
From here i tried if x=2 to cancel out the (Ax+B) term which results in C=0
this is where i believe an error has occured.
My other thinking was can I expand then factor out the x^2 and x and constant leaving the A and B and C in whatever they factor into and then do a system of equations.
My result this way is
A= 9/4, B =-9/2, C=-1/4
Kind regards
Homework Statement
Evaluate the following inde nite integral,
∫[itex]\frac{x^3-5x}{x^3-2x^2+4x-8}[/itex] dx
Homework Equations
I think I am right until i get to equating the equations when I do it the method I am taught in class I get c=0 and I don't think that is right. However when i put it into a system of equations with the coefficients i get fractions.
I would like to know what to do next. Thanks
The Attempt at a Solution
First the degree of numerator is same as the denomenator. So i do long division and end up with
∫1+ [itex]\frac{2x^2-9x+8}{x^3-2x^2+4x-8}[/itex]
Now decompose the fraction part into:
[itex]\frac{2x^2-9x+8}{(x^2+4)(x-2)}[/itex] =[itex]\frac{Ax+B}{(x^2+4)}[/itex]+[itex]\frac{C}{(x-2)}[/itex]
Then get a common denomenator for RHS
= [itex]\frac{(Ax+B)(x-2)+C(x^2+4)}{(x^2+4)(x-2)}[/itex]
From here i tried if x=2 to cancel out the (Ax+B) term which results in C=0
this is where i believe an error has occured.
My other thinking was can I expand then factor out the x^2 and x and constant leaving the A and B and C in whatever they factor into and then do a system of equations.
My result this way is
A= 9/4, B =-9/2, C=-1/4
Kind regards