| Exam Board | Edexcel |
| Module | C4 (Core Mathematics 4) |
| Topic | Integration by Substitution |
3. Use the substitution \(x = \sin \theta\) to show that, for \(| x | \leq 1\),
$$\int \frac { 1 } { \left( 1 - x ^ { 2 } \right) ^ { \frac { 3 } { 2 } } } \mathrm {~d} x = \frac { x } { \left( 1 - x ^ { 2 } \right) ^ { \frac { 1 } { 2 } } } + c \text {, where } c \text { is an arbitrary constant. }$$