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Firstly we remind ourselves of the integration by parts formula. The formula used to integrate u dv/dx with respect to x = uv - the integral of v du/dx with respect to x.
So the first thing we have t...

4/(x-3)*(x+2)/x= 4x+8/ x² -3x
sub in a for x4a+8/a²-3athen equate to 1: 4a+8/a²-3a=1Times the bottom half of the equation up4a+8=a²-3aThe move the 4a+8 acr...

Consider (x + 1)^2, where we halved the coefficient of x to obtain 1. This gives us x^2 + 2x + 1, which looks similar to our function, except it differs by a constant value of 6, hence, by adding 6 to (x ...

The key fact here is to remember the relationship between the gradients of lines which are parallel and perpendicular. Two lines that are parallel will always have the same gradient. So if we have a line ...

Initially this looks unlike all the other differentiation questions and seems unsolvable. However the expression 2^x can be rewritten in an equivalent form that will allow us to use the differentiation ru...