d^2x/dt = 1/sqrt(1-t^(2))

Question

with explained solution if possible.

Answer 1

Solve: d^2x/dt = 1/sqrt(1-t^(2))

Using standard integrals,

dx/dt = arcsin(t) + C

Integrating once more, (by parts)

x(t) = t.arcsin(t) + √(1 – t^2) + Ct + D