Substitution with exponential functions

A question is this type if and only if it requires substitution involving exponential expressions like u = eˣ or u = e^(f(x)) to simplify the integral.

4 questions · Standard +0.3

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Edexcel P3 2021 January Q9
4 marks Standard +0.3
9. Find
  1. \(\int \frac { 3 x - 2 } { 3 x ^ { 2 } - 4 x + 5 } \mathrm {~d} x\)
  2. \(\int \frac { \mathrm { e } ^ { 2 x } } { \left( \mathrm { e } ^ { 2 x } - 1 \right) ^ { 3 } } \mathrm {~d} x \quad x \neq 0\)
    VIIV SIHI NI JIIIM IONOOVIUV SIHI NI III M M I ON OOVI4V SIHI NI IIIYM ION OC
Edexcel C4 2007 June Q2
6 marks Standard +0.3
2. Use the substitution \(u = 2 ^ { x }\) to find the exact value of $$\int _ { 0 } ^ { 1 } \frac { 2 ^ { x } } { \left( 2 ^ { x } + 1 \right) ^ { 2 } } d x$$
OCR C4 2015 June Q5
6 marks Standard +0.3
5 By first using the substitution \(t = \sqrt { x + 1 }\), find \(\int \mathrm { e } ^ { 2 \sqrt { x + 1 } } \mathrm {~d} x\).
AQA Paper 1 Specimen Q8
7 marks Standard +0.3
8
  1. Given that \(u = 2 ^ { x }\), write down an expression for \(\frac { \mathrm { d } u } { \mathrm {~d} x }\)
    8
  2. Find the exact value of \(\int _ { 0 } ^ { 1 } 2 ^ { x } \sqrt { 3 + 2 ^ { x } } \mathrm {~d} x\) Fully justify your answer.
    [0pt] [6 marks]
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