Moderate -0.8 This is a straightforward definite integral requiring recognition of two standard logarithmic forms: ∫(1/x)dx = ln|x| and ∫(1/(2x+1))dx = (1/2)ln|2x+1|. The main steps are applying these standard results, substituting limits, and simplifying using log laws. While it requires careful algebraic manipulation at the end, there's no problem-solving or novel insight needed—just direct application of memorized techniques.
Use law for the logarithm of a product, quotient or power
M1
Obtain given answer correctly
A1
[6]
Integrate and state term $\ln x$ | B1 |
Obtain term of the form $k\ln(2x + 1)$ | M1 |
State correct term $-2\ln(2x + 1)$ | A1 |
Substitute limits correctly | M1 |
Use law for the logarithm of a product, quotient or power | M1 |
Obtain given answer correctly | A1 | [6]