Maths Integration

Hi, I'm not quite sure how to progress from here, I'm not even sure if trying to write the 4x - 1 in terms of u was even the right thing to do. Any help would be greatly appreciated

Have you managed to do it from the previous hint? You must change your integration limits when you switch to the u-variable (technically you can write x= ? for each limit and switch back to x after you integrate but that can get messy); the only other thing to do is remember your (pre-)GCSE fraction rules: (a+b)/c = (a/c) + (b/c) then you have something that is easy to integrate

Yes, I managed to do it, thank you for the reminder about the limits!

Is integration by substitution the only way to do this question? I thought in the exam, the substitution would be given?

Until a few years ago students were always expected to be able to come up with substitutions by themselves

In this case the required sub is fairly "obvious" - you want to make the denominator as simple as possible so you can divide by it, so the "obvious" thing to do it just call the bit in brackets "u" and see what happens. It helps that the numerator is linear and the derivative of u is just a constant, so the resulting integral comes out to something nice