Urgent PLz! =) (1 Viewer)

[Shady01]

Got an intergration exam tomorrow, there is only one question i cant do =(
Maybe im missing somthing, not sure?

Integral of [ (x^3+1)/(x^2+1) dx


cheers gl.

 

[Raginsheep]

∫(x³+1)/(x²+1) dx
=∫(x(x²+1)-x+1)/(x² dx
=∫(x-(x-1)/(x²+1) dx
=∫ x- x/(x²+1) + 1/(x²+1) dx

 

[pLuvia]

Usually if the degree of the numerator is greater than the degree of the denominator then you just use long division to simplify it.

 

[_ShiFTy_]

Divide, manipulate with the fraction you will get..

 

[Shady01]

sorry fellas you are gunna hve to spell this one out fer me.
Ragin I cant see what u've done between lines? I cann see how you split up x^3+1 that it sorry =(

 

[pLuvia]

∫(x³+1)/(x²+1) dx
=∫(x(x²+1)-x+1)/(x²+1) dx

He manipulated the question so it would be easier to integrate. He took an x out so that one of the equations would look like the denominator.

If you don't understand this way just use long division and you should get the same thing

 

[Shady01]

even LOng division that wont work x^3+1\ x^2+1
it ends up being like x-x.. on the top or somthing wackd?

 

[pLuvia]

Long division you would get
y=x+(-x+1)/(x²+1)
=x-x/(x²+1)+1/(x²+1)

Which is the same

 

[Raginsheep]

Since the difference in powers is so similar, its much easier and quicker to use manipulation rather than long division.

 

[Riviet]

When you manipulate, you are really performing long division, since you are constantly taking out factors and subtracting to compensate for added terms.

 

[Shady01]

ahhh ok so let me get this rite... wen u divide u get X with a remainder of -x+1 which goes over the oringal x^3+1 ? if thats it i get it now. cheers if not.. ahhhhhhhh! lol