Moderate -0.8 This is a straightforward application of the standard integral ∫(1/x)dx = ln|x| with a linear substitution (4x+1). Students need to recognize the reverse chain rule pattern, integrate to get (1/2)ln|4x+1|, then evaluate at the limits and simplify using log laws. While it requires careful algebraic manipulation of logarithms, it's a routine textbook exercise with no problem-solving insight needed, making it easier than average.
Integrate and obtain term of the form \(k\ln(4x+1)\)
M1
State correct term \(\frac{1}{2}\ln(4x+1)\)
A1
Substitute limits correctly
M1
Use law for the logarithm of a quotient or a power
M1
Obtain given answer correctly
A1
[5]
Integrate and obtain term of the form $k\ln(4x+1)$ | M1 |
State correct term $\frac{1}{2}\ln(4x+1)$ | A1 |
Substitute limits correctly | M1 |
Use law for the logarithm of a quotient or a power | M1 |
Obtain given answer correctly | A1 | [5]