11.5 Integration by Substitution

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Using the substitution $\sqrt{3x+1}$ , show that

$dx\int_{1}^{5} \sqrt{12x+4} e^{\sqrt{3x+1}} \, dx$

may be expressed in the form

$du\int_{a}^{b} k u^2 e^u \, du$

where $a$ , $b$ and $k$ are constants to be found.

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Hence find, by algebraic integration, the exact value of

$dx\int_{1}^{5} \sqrt{12x+4} e^{\sqrt{3x+1}} \, dx$

giving your answer in simplest form.

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11.5 Integration by Substitution Questions

Practise Edexcel A Level Maths 11.5 Integration by Substitution with exam-style questions for A Level Maths. 59 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.