Integrate (x2 - 1)/(x2 + 1): Lunar Guy's Question

[Lunar Guy]

1. Integrate on the interval [0, 1]: (x² - 1)/(x² + 1)

2. No relevant equations.

3.

S x²/(x² + 1) - [S 1/(x² + 1)] =

S (x² + 1) - 1/(x² + 1) - [(arctan x)] =

S -1 - [(arctan x)] =

-x - arctan x

I can plug in the numbers on my own, but I would like to know if what I've done so far is correct...

Thanks to anyone who reads this and answers it.

- Lunar Guy

 

[slider142]

How does ((x² + 1) - 1)/(x² + 1) become -1?

 

[a.a]

the (x^2 + 1) cancles
but where did u get x2/(x2 + 1) from?
x^2 - 1 = x - 1)(x+1)

 

[slider142]

the (x^2 + 1) cancles
but where did u get x2/(x2 + 1) from?
x^2 - 1 = x - 1)(x+1)

The (x² + 1) cancels to become 1 - (1/(x² + 1)), not -1.
He got x²/(x² + 1) from (a + b)/c = a/c + b/c.

 

[a.a]

so how does x^2/(x^2 +1) reduce to x^2 +1?

 

[slider142]

so how does x^2/(x^2 +1) reduce to x^2 +1?

That never happened. He skipped the step x² = x² + 1 - 1.

 

[FedEx]

Think its quite easy... Convert the neumerator in the form of the denominator by writing -1 as 1-2

 

[FedEx]

So now you get (xsquare + 1) - 2