Let f(x) = 7x + 18 (3x + 2)(x² + 4)

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

1. [B1] State or imply the form A/(3x+2) + (Bx+C)/(x²+4)
2. [M1] Use a correct method for finding a constant
3. [A1] Obtain one of A = 3, B = −1, C = 3
4. [A1] Obtain a second value
5. [A1] Obtain the third value
6. [B1] Integrate A/(3x+2) and obtain (A/3)ln(3x+2) or (A/3)ln|3x+2|
7. [M1] State a term of the form k ln (x²+4) from Bx/(x²+4) after splitting
8. [A1] Obtain correct integral of Bx/(x²+4) as (B/2)ln(x²+4)
9. [B1] Obtain correct integral of C/(x²+4) as (C/2)tan⁻¹(x/2)
10. [M1] Substitute limits correctly in an integral with at least two terms of the form a ln(3x+2), b ln(x²+4) and c tan⁻¹(x/2) and subtract in correct order
11. [A1] Obtain answer 3/2 ln 2 + 3/8 π, or exact 2-term equivalent