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## Homework Statement

Integrate at interval [0,T] (T and k are given real numbers) the

**2. Relevant equation**

[tex]_{0}^{T}\int \frac{sin(p)}{\sqrt{k+p}}\ dp[/tex]

## The Attempt at a Solution

[tex]\ Using\ substitution\ u\ =\ tan(p/2),\ results\ as\ :\ p\ =\ 2*arctan(u)\ \ ;\ \ dp\ =\ \frac{2}{1+u^2}\ du\ ;\ [/tex]

[tex]sin(p)\ =\ \frac{2*u}{1+u^2} ;\ cos(p)\ =\ \frac{1-u^2}{1+u^2} ;\ [/tex]

[tex]_{0}^{T}\int \frac{sin(p)}{\sqrt{k+p}}\ dp \ \ =\ _{0}^{2*arctan(T)}\int \frac{2*u*2}{(1+u^2)\ *\ \sqrt{k+2*arctan(u)}\ *\ (1+u^2)}\ du[/tex]

[tex]\ ¿\ Could\ someone\ get\ a\ better\ result\ ?[/tex]

(maybe with the substitution u = 2* sin(p) )

**...**