Integrate[x^2, x]

Integrate[ArcSin[k*x], x]

Integrate[1/Sqrt[a^2 - x^2], x]

D[ArcSin[x/a], x]

DSolve[{m*v'[t] == -C*v[t]}, v[t], t]

DSolve[{m*v'[t] == -C*v[t], v[0] == v0}, v[t], 
      t]

sol = 
      DSolve[{m*v'[t] == -C*v[t], v[0] == v0}, v[t], 
        t]

?Global`*

g^2 - 3*g /. g -> 10

?Global`g

v[t_, m_, C_, v0_] = v[t] /. sol

?Global`*

Plot[v[t, 1. , 0.1, 1. ], {t, 0. , 50. }, 
      AxesOrigin -> {0. , 0. }]

?Global`*

sol1 = 
      DSolve[{m*v'[t] == -C*v[t], v'[
              10] == - .5}, v[t], t]

v1[t_, m_, C_, v0_] = v[t] /. sol1

Plot[v1[t, 1. , 0.1, 1. ], {t, 0. , 50. }]

sol2 = 
      DSolve[{m*v'[t] == -m*g - C*v[t], v[0] == 0. }, 
        v[t], t]

v[t_, m_, g_, C_] = v[t] /. sol2

Plot[v[t, 1. , 9.8, 0.2], {t, 0. , 50. }, 
      AxesOrigin -> {0. , 0. }, PlotRange -> {0. , -50. }, 
      PlotStyle -> {RGBColor[1, 0, 0]}]

sol3 = 
      DSolve[{m*x''[t] == -k*x[t], 
          x[0] == x0, x'[0] == v0}, x[t], t]

x[t_, k_, m_, x0_, v0_] = x[t] /. sol3

Plot[x[t, 1, 1, 0.05, 0. ], {t, 0, 20. }]