Limit[x/(x-1)-1/Log[x],x->1]
Limit[(1+1/x^2)^x,x->Infinity]
Limit[Sqrt[n-Sqrt[n]]-Sqrt[n],n->Infinity]

D[Exp[x]+Exp[Exp[x]],x]
D[x^(x^x),x]
D[(Sin[x])^Cos[x],x]
D[Log[Cos[ArcTan[(Exp[x]-Exp[-x])/2]]],x]

D[1/(1-x^2),{x,60}]
D[(1+x)/Sqrt[1-x],{x,60}]

Integrate[x^2*a^x,x]
Integrate[(2x^2-5)/(x^4-5x^2+6),x]
Integrate[Log[x+Sqrt[1+x^2]],x]
Integrate[(Exp[2x]+1)/(Exp[x]+1),x]

Integrate[Sqrt[Exp[x]-1],{x,0,Log[2]}]
Integrate[x^2/Sqrt[x^2+a^2],{x,0,a}]
Integrate[(1/2*Sqrt[4x+1]+1)/x,{x,0,1}]
Integrate[x*y^2,{x,0,1},{y,x^2,x}]
Integrate[x*y*z,{x,0,1},{y,0,x},{z,0,x+y}]
Integrate[x*Sqrt[y]*Boole[x^2<=y<=Sqrt[x]],{x,0,Infinity},{y,0,Infinity}]

y[x_]:=a*Cosh[x/a]
Integrate[Sqrt[1+y'[x]^2],{x,-a,a}]
ClearAll["Global`*"]

Series[Log[(1+x)/(1-x)],{x,0,5}]
Series[Cos[x]*Cos[y],{x,0,5},{y,0,5}]

DSolve[{y'[x]==y[x]+x,y[0]==1},y[x],x]
DSolve[{x'[t]==2*x[t]-y[t]+z[t],y'[t]==2*x[t]+2*y[t]-z[t],z'[t]==x[t]+2*y[t]-z[t]},{x[t],y[t],z[t]},t]

DSolve[(y+z)*D[u[x,y,z],x]+(z+x)*D[u[x,y,z],y]+(x+y)*D[u[x,y,z],z]==0,u[x,y,z],{x,y,z}]
DSolve[(x*y^3-2x^4)*D[u[x,y],x]+(3y^4-x^3*y)*D[u[x,y],y]==9*u[x,y]*(x^3-y^3),u[x,y],{x,y}]