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fricas
integrate(sin(sqrt(x*x)),x)

\label{eq1}-{2 \over{{{\tan \left({{\sqrt{{x}^{2}}}\over 2}\right)}^{2}}+ 1}}(1)
Type: Union(Expression(Integer),...)
fricas
D(%,x)

\label{eq2}{2 \  x \ {\tan \left({{\sqrt{{x}^{2}}}\over 2}\right)}}\over{{{\sqrt{{x}^{2}}}\ {{\tan \left({{\sqrt{{x}^{2}}}\over 2}\right)}^{2}}}+{\sqrt{{x}^{2}}}}(2)
Type: Expression(Integer)
fricas
%-sin(sqrt(x*x))

\label{eq3}{\left(
\begin{array}{@{}l}
\displaystyle
-{{\sqrt{{x}^{2}}}\ {\sin \left({\sqrt{{x}^{2}}}\right)}\ {{\tan \left({{\sqrt{{x}^{2}}}\over 2}\right)}^{2}}}+{2 \  x \ {\tan \left({{\sqrt{{x}^{2}}}\over 2}\right)}}- 
\
\
\displaystyle
{{\sqrt{{x}^{2}}}\ {\sin \left({\sqrt{{x}^{2}}}\right)}}
(3)
Type: Expression(Integer)
fricas
normalize %

\label{eq4}0(4)
Type: Expression(Integer)
fricas
)trace INTEF )math
Packages traced: ElementaryIntegration(Integer,Expression(Integer)) Parameterized constructors traced: INTEF integrate(sin(sqrt(x*x)),x)
1<enter ElementaryIntegration.lfintegrate,43 : x 2tan(-) 2 arg1= ----------- x 2 tan(-) + 1 2 arg2= x 2<enter ElementaryIntegration.lfintegrate,43 : arg1= 0 arg2= x 2>exit ElementaryIntegration.lfintegrate,43 : 0 1>exit ElementaryIntegration.lfintegrate,43 : 2 - ----------- x 2 tan(-) + 1 2

\label{eq5}-{2 \over{{{\tan \left({{\sqrt{{x}^{2}}}\over 2}\right)}^{2}}+ 1}}(5)
Type: Union(Expression(Integer),...)
fricas
D(%,x)

\label{eq6}{2 \  x \ {\tan \left({{\sqrt{{x}^{2}}}\over 2}\right)}}\over{{{\sqrt{{x}^{2}}}\ {{\tan \left({{\sqrt{{x}^{2}}}\over 2}\right)}^{2}}}+{\sqrt{{x}^{2}}}}(6)
Type: Expression(Integer)
fricas
%-sin(sqrt(x*x))

\label{eq7}{\left(
\begin{array}{@{}l}
\displaystyle
-{{\sqrt{{x}^{2}}}\ {\sin \left({\sqrt{{x}^{2}}}\right)}\ {{\tan \left({{\sqrt{{x}^{2}}}\over 2}\right)}^{2}}}+{2 \  x \ {\tan \left({{\sqrt{{x}^{2}}}\over 2}\right)}}- 
\
\
\displaystyle
{{\sqrt{{x}^{2}}}\ {\sin \left({\sqrt{{x}^{2}}}\right)}}
(7)
Type: Expression(Integer)
fricas
normalize %

\label{eq8}0(8)
Type: Expression(Integer)
fricas
)trace INTEF )off
Nothing is traced now.
integrate(sin(sqrt(x*x)),x)

\label{eq9}-{2 \over{{{\tan \left({x \over 2}\right)}^{2}}+ 1}}(9)
Type: Union(Expression(Integer),...)
fricas
D(%,x)

\label{eq10}{2 \ {\tan \left({x \over 2}\right)}}\over{{{\tan \left({x \over 2}\right)}^{2}}+ 1}(10)
Type: Expression(Integer)
fricas
%-sin(sqrt(x*x))

\label{eq11}{{{\left(-{{\tan \left({x \over 2}\right)}^{2}}- 1 \right)}\ {\sin \left({\sqrt{{x}^{2}}}\right)}}+{2 \ {\tan \left({x \over 2}\right)}}}\over{{{\tan \left({x \over 2}\right)}^{2}}+ 1}(11)
Type: Expression(Integer)
fricas
normalize %
x - x ----- 2
>> Error detected within library code: Hidden constant detected




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