\((\text{i})\) Given \(\displaystyle \int _{ 0 }^{ a }{ 6{ e }^{ 2x }+x } \, dx=42\), show that \[a=\dfrac{1}{2}\ln\left (15-\dfrac{a^2}{6}\right ).\]

\((\text{ii})\) Use an iterative formula to find \(a\), correct to **3 decimal places**. Use a starting value of 1 and show the result of each iteration.

**Input \(1000 \times\) your answer to part \((\text{ii})\).**

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