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asinh

Run Example
(%i1)expr:asinh((L/2-z)/sqrt(x^2+y^2));
                                       L
                                       - - z
                                       2
(%o1)                        asinh(-------------)
                                         2    2
                                   sqrt(y  + x )
(%i2) ee:x^2;
                                       2
(%o2)                                 x
(%i3) diff(expr,x);
                                       L
                                    x (- - z)
                                       2
(%o3)                  - -------------------------------
                                            L     2
                                           (- - z)
                           2    2 3/2       2
                         (y  + x )    sqrt(-------- + 1)
                                            2    2
                                           y  + x
(%i4) 
Run Example
display2d:false;

(%o1) false
(%i2) 
I1:((4*a^2*x^2+1)^(3/2)/(12*a^2))/(E*I);

(%o2) (4*a^2*x^2+1)^(3/2)/(12*a^2*E*I)
(%i3) 
I2:(a*(-asinh(2*abs(a)*x)/(64*a^2*abs(a)) +x*(4*a^2*x^2+1)^(3/2)/(16*a^2)-x*sqrt(4*a^2*x^2+1)/(32*a^2)))/(E*I);

(%o3) a*(-asinh(2*abs(a)*x)/(64*a^2*abs(a))
        +x*(4*a^2*x^2+1)^(3/2)/(16*a^2)-x*sqrt(4*a^2*x^2+1)/(32*a^2))
       /(E*I)
(%i4) 
I3:(-asinh(2*abs(a)*x)/(64*a^2*abs(a))+x*(4*a^2*x^2+1)^(3/2)/(16*a^2)-x*sqrt(4*a^2*x^2+1)/(32*a^2))/(E*I);

(%o4) (-asinh(2*abs(a)*x)/(64*a^2*abs(a))+x*(4*a^2*x^2+1)^(3/2)/(16*a^2)
                                         -x*sqrt(4*a^2*x^2+1)/(32*a^2))
       /(E*I)
(%i5) 
I4:(a^2*(asinh(2*abs(a)*x)/(512*a^4*abs(a))+x^3*(4*a^2*x^2+1)^(3/2)/(24*a^2)-x*(4*a^2*x^2+1)^(3/2)/(128*a^4)+x*sqrt(4*a^2*x^2+1)/(256*a^4)))/(E*I);

(%o5) a^2*(asinh(2*abs(a)*x)/(512*a^4*abs(a))
          +x^3*(4*a^2*x^2+1)^(3/2)/(24*a^2)-x*(4*a^2*x^2+1)^(3/2)/(128*a^4)
          +x*sqrt(4*a^2*x^2+1)/(256*a^4))
       /(E*I)
(%i6) 
I5:(a*(x^2*(4*a^2*x^2+1)^(3/2)/(20*a^2)-(4*a^2*x^2+1)^(3/2)/(120*a^4)))/(E*I);

(%o6) a*(x^2*(4*a^2*x^2+1)^(3/2)/(20*a^2)-(4*a^2*x^2+1)^(3/2)/(120*a^4))/(E*I)
(%i7) 
I0:((asinh(2*abs(a)*x)/(4*abs(a))+x*sqrt(4*a^2*x^2+1)/2))/(E*I);

(%o7) (asinh(2*abs(a)*x)/(4*abs(a))+x*sqrt(4*a^2*x^2+1)/2)/(E*I)
(%i8) 
 	I0:subst(X,x,I0);

(%o8) (asinh(2*abs(a)*X)/(4*abs(a))+X*sqrt(4*a^2*X^2+1)/2)/(E*I)
(%i9) 
I1:subst(X,x,I1);

(%o9) (4*a^2*X^2+1)^(3/2)/(12*a^2*E*I)
(%i10) 
I2:subst(X,x,I2);

(%o10) a*(-asinh(2*abs(a)*X)/(64*a^2*abs(a))
         +X*(4*a^2*X^2+1)^(3/2)/(16*a^2)-X*sqrt(4*a^2*X^2+1)/(32*a^2))
        /(E*I)
(%i11) 
I3:subst(X,x,I3);

(%o11) (-asinh(2*abs(a)*X)/(64*a^2*abs(a))+X*(4*a^2*X^2+1)^(3/2)/(16*a^2)
                                          -X*sqrt(4*a^2*X^2+1)/(32*a^2))
        /(E*I)
(%i12) 
I4:subst(X,x,I4);

(%o12) a^2*(asinh(2*abs(a)*X)/(512*a^4*abs(a))
           +X^3*(4*a^2*X^2+1)^(3/2)/(24*a^2)-X*(4*a^2*X^2+1)^(3/2)/(128*a^4)
           +X*sqrt(4*a^2*X^2+1)/(256*a^4))
        /(E*I)
(%i13) 
I5:subst(X,x,I5);

(%o13) a*(X^2*(4*a^2*X^2+1)^(3/2)/(20*a^2)-(4*a^2*X^2+1)^(3/2)/(120*a^4))
        /(E*I)
(%i14) 
Run Example
(40000/X)/(asinh(725)^2);
                                     40000
(%o1)                            -------------
                                      2
                                 asinh (725) X
(%i2) 

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