You are certainly correct, although morally this is really equivalent to IBP since that result come from the product rule and integration by parts is simply a formalisation of the 'reverse product rule'. Sometimes showing more steps can be a good idea as it means we are more certain to receive method marks and, even if the shortcut is mathematically correct, it can also reduce the risk of unfriendly marking errors! - Rowan
1 (iii) (b) IBP not necessary since
∫e^x[f(x) + f'(x)]dx = e^xf(x) + c
You are certainly correct, although morally this is really equivalent to IBP since that result come from the product rule and integration by parts is simply a formalisation of the 'reverse product rule'. Sometimes showing more steps can be a good idea as it means we are more certain to receive method marks and, even if the shortcut is mathematically correct, it can also reduce the risk of unfriendly marking errors! - Rowan