Q:

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- May 15th 2007, 07:52 PMqbkr21Partial Fraction
Q:

- May 15th 2007, 07:54 PMThePerfectHacker
Factor out a 9.

Meaning,

1/(9+x^2) can be written as

1/9 * 1/(1+(x/3)^2)

Now let t=x/3 - May 15th 2007, 07:56 PMJhevon
- May 15th 2007, 07:59 PMqbkr21Re:
Thanks Guys!:)

- May 16th 2007, 05:40 AMSoroban
Hello, everyone!

A question:

Doesn't anyone teach the**general**formulas for inverse trig integrals?

. . . . . .du

. . ∫ --__---------__- . = . arcsin(u/a) + C

. . . .√aČ - uČ

. . . . . .du

. . ∫ ---------- . = . (1/a)·arctan(u/a) + C

. . . .uČ + aČ

. . . . . . .du

. . I ----__--------__- . = . (1/a)·arcsec(u/a) + C

. . . .u√uČ - aČ

A half-century ago, my professor derived these formulas for us.

. . We have*never*had to factor-out-4 or factor-out-9.

[rant]

I've made this query at other math sites.

No one has ever thanked me for these streamlined formulas.

Instead, someone replies with something like:

"I'd rather have my students*understand*the concepts

. . rather than**memorizing a list of formulas**"

as if memorizing is a Bad Thing.

My first response has been:

If you've already**memorized**a formula with uČ + 1

. . why not expand it to include the "a"?

They usually reply with hints that I'm a formula-happy moron.

(Have they ever seen any of my posts?

Isn't*Understanding*the main feature of all my explanations?)

And then I must respond with something like:

If Understanding is the most important issue,

. . then we must not**memorize**the Quadratic Formula.

Instead, we make the student complete-the-square every time.

Then someone says, "What's wrong with completing-the-square?

I'd rather have them*understand*the procedure, than just*memorize a formula*."

Then I must explain the Philosophy of Learning.

When we*learn*a new fact, we in fact*memorize*it.

. . Yes, we "commit it to memory" for future use.

Then (and here's the important part)*. . . we move on*.

We add the formula/shortcut to our arsenal (in the war against our own ignorance)

. . and progress to bigger and better things.

And it is hoped that we retain the reasoning behind the formulas/shortcuts.

We do not draw a line in the sand and say, "This is far enough!

. . From now on, everything will be*derived*... no more blind memorization!"

If Memorization is a misdemeanor, then 2 Ś 3 .= .6 is at least a felony.

. . After all, it can__derived__from: 3 + 3 .= .6

In fact, throw out the addition tables!

. . {◊ ◊ ◊} + {◊ ◊ ◊} .= .{◊ ◊ ◊ ◊ ◊ ◊}

. . . 1-2-3 . . . . 1-2-3 . - . . .1*2*3-4-5*6

We can always stop and "count apples", right?

[/rant]

- May 16th 2007, 06:46 AMcurvatureYou don't need partial fraction
You don't need partial fraction. Just use the substitution rule.

- May 16th 2007, 10:19 AMqbkr21Re:
Re:

- May 17th 2007, 06:55 AMcurvatureThe integral can be found as follows
The integral can be evaluated as follows:

- May 30th 2007, 12:21 PMKrizalid
- Jun 1st 2007, 07:05 AMcurvaturepartial fraction
partial fraction