how to solve

i tried by parts but its not not working

any ideas

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- June 24th 2011, 03:36 PMtransgalacticroot integral question
how to solve

i tried by parts but its not not working

any ideas - June 24th 2011, 03:41 PMPlatoRe: root integral question
- June 24th 2011, 03:48 PMtransgalacticRe: root integral question
what method they used?

- June 24th 2011, 03:50 PMPlatoRe: root integral question
- June 24th 2011, 04:33 PMTheCoffeeMachineRe: root integral question
See this. If you can calculate or know

then doing the integral is very easy. - June 24th 2011, 09:51 PMchisigmaRe: root integral question
In any 'manual' You can find the 'derivative' ...

(1)

... so that is...

(2)

On WolframAlpha [I wonder why...] a different and more complicated formula is reported...

Wolfram Mathematica Online Integrator

Anyway following TCM we obtain...

(3)

Kind regards

- June 25th 2011, 06:34 AMSorobanRe: root integral question
Hello, transgalactic!

Quote:

Use "Trig Substitution".

Evidently, you aren't familiar with it . . .

Let:

Note that:

. . . . . . . .

Substitute: .

. . . . . .

. . . . . . .[1]

Back-substitute: .

is in a right triangle with:

Pythagorus gives us: .

Hence: .

We have: .

Substitute into [1]:

. .

. .

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

I have no idea why so many textbooks and sources use

. . which requires extra steps and looks more intimidating.

- June 25th 2011, 06:36 AMHallsofIvyRe: root integral question
- June 25th 2011, 07:10 AMtom@ballooncalculusRe: root integral question
Wow!! Absolutely everyone has mis-read the a as a^2! (Rofl)

Not massively consequential, but an excuse for some pictures...

http://www.ballooncalculus.org/draw/internal/ten.png

Then, swap the inner function...

http://www.ballooncalculus.org/draw/internal/tena.png

... where (key in spoiler) ...

__Spoiler__:

__Spoiler__:

_________________________________________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote! - June 25th 2011, 09:12 AMDevenoRe: root integral question
i believe the substitution that actually works is