2.2 \(\int \frac {x \arcsin (x)}{\sqrt {1-x^2}}\,dx\)

2.2.1 Mathematica

Clear[x] 
Integrate[(x ArcSin[x])/Sqrt[1 - x^2], x]
 

\[ x-\sqrt {1-x^2} \sin ^{-1}(x) \]

2.2.2 Rubi

<< Rubi` 
Clear[x] 
Int[(x ArcSin[x])/Sqrt[1 - x^2], x]
 

\[ x-\sqrt {1-x^2} \sin ^{-1}(x) \]

2.2.3 Maple

restart; 
integrand:=x*arcsin(x)/sqrt(1-x^2); 
int(integrand,x); 
latex(%)
 

\[ x-\arcsin \left ( x \right ) \sqrt {-{x}^{2}+1} \]

2.2.4 Fricas

set output tex off 
setSimplifyDenomsFlag(true) 
ii:=integrate(x*asin(x)/sqrt(1-x^2),x) 
latex(ii)
 

\[ -{{\arcsin \left ( {x} \right )} \ {\sqrt {{-{{x} \sp {2}}+1}}}}+x \]

2.2.5 Maxima

ii : integrate(x*asin(x)/sqrt(1-x^2),x); 
tex(ii);
 

\[ x-\sqrt {1-x^2}\,\arcsin x \]

2.2.6 XCAS

ii := integrate(x*asin(x)/sqrt(1-x^2),x); 
latex(ii)
 

\[ -\sqrt {-x^{2}+1} \arcsin x+x \]

2.2.7 Sympy

>python 
Python 3.7.3 (default, Mar 27 2019, 22:11:17) 
[GCC 7.3.0] :: Anaconda, Inc. on linux 
 
from sympy import * 
x = symbols('x') 
ii=integrate(x*asin(x)/sqrt(1-x**2),x) 
latex(ii)
 

\[ x - \sqrt {1 - x^{2}} \operatorname {asin}{\left (x \right )} \]

2.2.8 MuPad

evalin(symengine,'int(x*asin(x)/sqrt(1-x^2),x)')
 

\[ \text {did not solve} \]