| Exam Board | Edexcel |
| Module | C4 (Core Mathematics 4) |
| Year | 2014 |
| Session | January |
| Topic | Integration by Parts |
2. (i) Find
$$\int x \cos \left( \frac { x } { 2 } \right) \mathrm { d } x$$
(ii) (a) Express \(\frac { 1 } { x ^ { 2 } ( 1 - 3 x ) }\) in partial fractions.
(b) Hence find, for \(0 < x < \frac { 1 } { 3 }\)
$$\int \frac { 1 } { x ^ { 2 } ( 1 - 3 x ) } \mathrm { d } x$$