| Exam Board | Edexcel |
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| Module | C34 (Core Mathematics 3 & 4) |
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| Year | 2017 |
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| Session | October |
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| Topic | Integration by Substitution |
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5. (i) Find
$$\int \left( ( 3 x + 5 ) ^ { 9 } + \mathrm { e } ^ { 5 x } \right) \mathrm { d } x$$
(ii) Given that \(b\) is a constant greater than 2 , and
$$\int _ { 2 } ^ { b } \frac { x } { x ^ { 2 } + 5 } \mathrm {~d} x = \ln ( \sqrt { 6 } )$$
use integration to find the value of \(b\).