| Exam Board | SPS |
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| Module | SPS FM (SPS FM) |
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| Year | 2020 |
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| Session | June |
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| Topic | Integration by Substitution |
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2. Show that the substitution \(x = \sin \theta\) transforms
$$\int \frac { 1 } { \left( 1 - x ^ { 2 } \right) ^ { \frac { 3 } { 2 } } } d x$$
to
$$\int \sec ^ { 2 } \theta d \theta$$
and hence find
$$\int \frac { 1 } { \left( 1 - x ^ { 2 } \right) ^ { \frac { 3 } { 2 } } } d x$$