| Exam Board | Edexcel |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2022 |
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| Session | January |
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| Topic | Integration by Substitution |
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3. (i) Find, in simplest form,
$$\int ( 2 x - 5 ) ^ { 7 } \mathrm {~d} x$$
(ii) Show, by algebraic integration, that
$$\int _ { 0 } ^ { \frac { \pi } { 3 } } \frac { 4 \sin x } { 1 + 2 \cos x } \mathrm {~d} x = \ln a$$
where \(a\) is a rational constant to be found.