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Is this one's result - ?

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- May 30th 2006, 03:12 PMnirva2 Integral questions
1.

2.

Is this one's result - ? - May 30th 2006, 03:17 PMThePerfectHackerQuote:

Originally Posted by**nirva**

then, Thus, you have,

becomes,

Thus,

- May 30th 2006, 03:30 PMThePerfectHackerQuote:

Originally Posted by**nirva**

This involves trigonomteric substitution.

You have,

Rationalize,

Let,

Then,

Thus, express integrand as,

Thus, substitute the previous equations,

Thus,

Now, just determine this new integral.

Use trigonometric identities thus,

Thus,

Let,

Then,

Express integrand as,

Make the above substitutions,

Thus,

Substitute for to get,

Thus,

Substitute for to get,

Thus,

- May 31st 2006, 12:15 AMTD!
I find the same answer but I don't see why you do the rationalizing and rewriting if the substitution t = tan(u) works immediately.

Which is the same as your last step, yeilding:

- May 31st 2006, 02:20 PMThePerfectHackerQuote:

Originally Posted by**TD!**

- May 31st 2006, 02:23 PMTD!
My beaty lies in compactness :D

- June 1st 2006, 02:02 PMtopsquarkQuote:

Originally Posted by**TD!**

-Dan - June 1st 2006, 02:07 PMTD!
And not only beautiful, also closed and bounded! :D