yep, integrate each component seperately, but remember there will be a constant of integration for each component that you integrate. You can find the value of these constants if you have some initial conditions, otherwise just leave them as arbitrary constants, though in practice most problems will have conditions that allow you to find the values of the constants.
Magnus Konow died in 1972.
Magnus Konow was born in 1887.
Henri Konow died in 1939.
Henri Konow was born in 1862.
Karsten Konow was born in 1918.
Karsten Konow died in 1943.
August Konow was born in 1780.
August Konow died in 1873.
Thomas Konow was born in 1796.
Thomas Konow died in 1881.
Fredrik Ludvig Konow died in 1954.
Fredrik Ludvig Konow was born in 1864.