[tex] 2u du=e^{x} dx [tex]

I finally get to

so if this is right

can somebody help me with hte second part of the last integral

and if it's wrong somekind of solution

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- Jan 24th 2008, 03:40 PMakhayoonrational substiution integral

[tex] 2u du=e^{x} dx [tex]

I finally get to

so if this is right

can somebody help me with hte second part of the last integral

and if it's wrong somekind of solution - Jan 24th 2008, 03:53 PMJhevon
i get something different for the integral. by the way, i don't like the substitution you made because , but anyway, you'd get something like if we say

an alternative is to use two substitutions. first and then and you'll get a similar integral to the one above

if you're still interested, completing the square coupled with substitution can take care of your original integral - Jan 24th 2008, 09:02 PMSoroban
Hello, akhayoon!

Your substitution should have come out like Jhevon's . . .

Quote:

Let

Substitute: .

Back-substitute: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Here's another method . . . it's either brilliant or incredibly stupid.

Let

Substitute: .

Back-substitute

We have: .

This is a right triangle with: .

Hence: .

So we have: .

. .

. .

You mission (should you decide to accept it)

. . is to prove that my two answers are equivalent.

. - Jan 25th 2008, 12:50 PMJhevon
i say brilliant! so crazy, it's brilliant! ...though not for the faint of heart, or those new to the world of integrals. how did you discover such a substitution? was the integral given in a "special form"?

Quote:

You mission (should you decide to accept it)

. . is to prove that my two answers are equivalent.

.

- Jan 25th 2008, 01:01 PMKrizalid
One can play with trig. sub. as many times as necessary.

700% personal opinion, I don't like trig. substitutions, some times it turns the integrand into a mess, but it depends of the problem.

I prefer workin' with algebra, you can get faster solutions, especially the reciprocal substitution, which can turn a nasty integral, into a cute one. (Not always, of course.)