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

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

(-(a*x*Sqrt[1 + x^2/a^2]) + (a^2 + 2*x^2)*ArcSinh[x/a])/4


Integrate[x*ArcSinh[x/a], x] ==
(-(a*x*Sqrt[1 + x^2/a^2]) + (a^2 + 2*x^2)* ArcSinh[x/a])/4



                    x
Integrate[x ArcSinh[-], x] == 
                    a

                2
               x        2      2          x
-(a x Sqrt[1 + --]) + (a  + 2 x ) ArcSinh[-]
                2                         a
               a
--------------------------------------------
                     4

Time to compute: 0.05 second

Spread the word: