I cannot figure out how to integrate this expression. A root of a root? Trig substitution does not work. My ti 89 says answer is

(4/15)(sqrt(x)+2)(3sqrt(x)-4). Any help is appreciated.

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- Aug 5th 2006, 10:06 AMspeedengineHelp Integrate: sqrt(2+x^(1/2))
I cannot figure out how to integrate this expression. A root of a root? Trig substitution does not work. My ti 89 says answer is

(4/15)(sqrt(x)+2)(3sqrt(x)-4). Any help is appreciated. - Aug 5th 2006, 10:57 AMSoroban
Hello, speedengine!

Quote:

Answer: .

With "nested" radicals, it often works if we let equal*something inside*.

Let:

Substitute: .

Factor out

Factor out

Since , we have: .

. . .

- Aug 5th 2006, 11:57 AMspeedengine
Hey Soroban,

Awesome! Defining x in terms of u is where I was missing. Thanks a bunch!