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This question often throws maths students off fairly easily as they are generally not taught the integral of lnx, and do not usually realise that integration by parts can be used for anything, as you can ...

Firstly, we need to differentiate the equation to find an equation for the gradient of the line.dy/dx = 6x-12We know the original graph was quadratic, and therefore only has one stationary point. This is ...

3l²mn + nl²m - 5mn²l + l²nm + 2n²ml - mn²
The first step is to ask yourself if there is anything that could help you simplify the equ...

∫  Cosec (x)/Sec (x) dx∫  [1/Sin (x)]/ [1/Cos (x)] dx∫  [1/Sin (x)] * [Cos (x)] dx∫  Cot (x)= ln [Sin (x)] + c

We can write the two numbers as x and 1000-x, because x+(1000-x) = 1000 for any x we pick. Now we want to maximise the product x(1000-x); expanding the brackets gives us 1000x-x² which is easie...