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Integrate...

I'm having trouble Integrating this formula..

y=\frac{1}{1+x^2}

any help would be appreciated

Reply 1

aster100

The answer is arctan(x) + C

Reply 2

kabbers

substitute

x = \tan \theta

Reply 3

aster100

kabbers

substitute

x = \tan \theta

How did you just "know" that?

Reply 4

kabbers

aster100

How did you just "know" that?

experience.. it is also done to death in FP2 :p:

Reply 5

silent ninja

You are looking for a trig function such that 1+(something)^2 will give you a single function. So in this case,

u=tan\theta

cot\theta

will work because

1+tan^2\theta= sec^2\theta

, and similar for

Unparseable latex formula:

cot\thet

.
You could also try a hyperbolic function such as

sinh\theta

Reply 6

aster100

Well I knew the standard result. I wasn't sure, until just now, how you thought up such an efficient substitution.

Reply 7

silent ninja

aster100

Well I knew the standard result. I wasn't sure, until just now, how you thought up such an efficient substitution.

Dont know if you seen my post above?
It's obvious, but strangely, never pointed out in my book anyway. Works especially well for square roots.

Reply 8

aster100

silent ninja

Dont know if you seen my post above?
It's obvious, but strangely, never pointed out in my book anyway. Works especially well for square roots.

nice

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