Integrate √(5+4x-x^2)

I dont even know where to begin. Any ideas?

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- Oct 13th 2010, 08:31 PM #1

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- Oct 13th 2010, 08:37 PM #2

- Oct 13th 2010, 08:52 PM #3

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When you see something with $\displaystyle x^2$ as the largest power or in any case where you may complete the square e.g $\displaystyle x^4+2x^2+3=(x^2+1)^2+2 $. Then you want use a trig substitution. A trig substition involves a squared term and a constant. This is useful when the whole term is bracketed by a power which makes the normal integration complex.

For your question

$\displaystyle \int \sqrt{5+4x-x^2} = \int \sqrt{9-(x-2)^2}$

let $\displaystyle x-2=\frac{sinx}{3} $

And the rest is just a normal substitution

Also there are 3 different trig substitutions sin, tan and sec. see if you can tell when to use each one as each one of them have a specific time and place to be used.