2.1.4.5 ✓ Mathematica. Time used: 0.004 (sec). Leaf size: 12

ode=D[x[t],t]==1/Sqrt[1+t^2]; 
ic={x[1]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \text {arcsinh}(t)-\text {arcsinh}(1) \end{align*}