Find \( \int (2 + 5x) \; dx - Edexcel - A-Level Maths Pure - Question 3 - 2008 - Paper 1

To integrate the expression ( 2 + 5x ), we separate the integration of each term:

[ \int (2 + 5x) ; dx = \int 2 ; dx + \int 5x ; dx ]

For the first term: [ \int 2 ; dx = 2x ]

For the second term, using the power rule of integration: [ \int 5x ; dx = 5 \cdot \frac{x^{2}}{2} = \frac{5}{2}x^{2} ]

Combining both results, we have:

[ \int (2 + 5x) ; dx = 2x + \frac{5}{2}x^{2} + c ]

where ( c ) is the constant of integration.