integrals.wolfram.com   Use one of Mathematica's 2500+ functions FREE online

Wolfram Mathematica Online Integrator
The world's only full-power integration solver
∫

(x*(8 + 6*x + x^2) - 8*Sqrt[x]*Sqrt[4 + x]*ArcSinh[Sqrt[x]/2])/(2*Sqrt[x*(4 + x)])


Integrate[Sqrt[4*x + x^2], x] ==
(x*(8 + 6*x + x^2) - 8*Sqrt[x]*Sqrt[4 + x]* ArcSinh[Sqrt[x]/2])/(2*Sqrt[x*(4 + x)])



                      2
Integrate[Sqrt[4 x + x ], x] == 

               2
(x (8 + 6 x + x ) - 8 Sqrt[x] Sqrt[4 + x] 
 
             Sqrt[x]
     ArcSinh[-------]) / (2 Sqrt[x (4 + x)])
                2

Time to compute: 0.09 second

Spread the word: