Show that ∫(from 1 to 4) (x + 4)/(x(x + 2)) dx = ln(k), where k is a rational number to be found.

Mark scheme

Marking points from the official mark scheme. The mark or mark type is shown in brackets.

1. M1 for attempting to resolve (x + 4)/(x(x + 2)) into partial fractions.
2. A1 for correctly finding A = 2 and B = -1, or equivalent form (e.g. 2/x - 1/(x+2)).
3. M1 for integrating their partial fractions. Expect A ln|x| + B ln|x+2|.
4. A1 for correctly integrating to 2 ln|x| - ln|x+2|.
5. M1 for correct application of limits to their integrated expression (upper limit - lower limit).
6. A1 for k = 32/9. (Must show ln(32/9) or equivalent steps leading to it).