Moderate -0.5 This is a straightforward single application of integration by parts with standard functions (polynomial × exponential) and simple limits. It requires only routine technique with no problem-solving insight, making it easier than average, though not trivial since it still requires correct execution of the integration by parts formula and evaluation at limits.
State first step of the form \(kxe^{2x} + \int ke^{2x} dx\)
M1
Complete the first step correctly
State first step of the form $kxe^{2x} + \int ke^{2x} dx$ | M1 | Complete the first step correctly | A1 | Substitute limits correctly having attempted the further integration of $ke^{2x}$ | M1 | Obtain answer $\frac{1}{4}(e^2 + 1)$ or exact equivalent of the form $ae^2 + b$, having used $e^0 = 1$ throughout | A1 | **[4]**