Irrational Integral (1 Viewer)

[juantheron]

 

[zeebobDD]

http://www.wolframalpha.com/input/?i=integrate+sqrt(x+++sqrt(x^2+2))

 

[fortune_cookie]

http://www.wolframalpha.com/input/?i=integrate+sqrt(x+++sqrt(x^2+2))

It definately looked like the u=sqrt(x^2+2) would be the first thing to do.

After that it falls out very easy.

 

[iSplicer]

Immediate instinct would be to use trig subst, but letting u = [everything under the first root]<everything under="" the="" first="" bracket=""> ie x + sqrt[x^2 +2] seems to work =]

Edit: beaten to it! =)</everything>

 

[Fus Ro Dah]

http://www.wolframalpha.com/input/?i=integrate+sqrt(x+++sqrt(x^2+2))

I really don't think throwing a wolfram link is the best way to answer juantheron's question, as it is a nontrivial integral.

 

[iSplicer]

I really don't think throwing a wolfram link is the best way to answer juantheron's question, as it is a nontrivial integral.

Clicking 'show steps' shows the entire process all the way up to the answer?

 

[Fus Ro Dah]

Clicking 'show steps' shows the entire process all the way up to the answer?

Quite often, Wolfram does not use the optimal way to finding the solution, and rather uses the 'Brute Force' method as opposed to elegant ones.

 

[iSplicer]

Quite often, Wolfram does not use the optimal way to finding the solution, and rather uses the 'Brute Force' method as opposed to elegant ones.

Fair call. Wasn't aware of that, I don't think that feature was a huge thing when I did my HSC, haha.

btw, love your username!

 

[juantheron]

Thanks friends I have solved in same way.....

 

[zeebobDD]

Quite often, Wolfram does not use the optimal way to finding the solution, and rather uses the 'Brute Force' method as opposed to elegant ones.

yeah your right.. but the steps for juans question doesnt seem too difficult