| Exam Board | CAIE |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2014 |
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| Session | November |
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| Topic | Integration by Substitution |
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10 By first using the substitution \(u = \mathrm { e } ^ { x }\), show that
$$\int _ { 0 } ^ { \ln 4 } \frac { \mathrm { e } ^ { 2 x } } { \mathrm { e } ^ { 2 x } + 3 \mathrm { e } ^ { x } + 2 } \mathrm {~d} x = \ln \left( \frac { 8 } { 5 } \right)$$