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a) Integrate ln(x) by parts: u = ln(x), dv/dx = 1, du/dx = 1/x, v = x int(udv/dx) = uv - int(du/dx * v) = ln(x)/x - x so int(ln(x) + 1/x - x) = ln(x)/x - x + ln(x) + x^2 + Cb) y = ln(x)/x - x + l...

Since our function is a product of two "mini-functions" of x, we are able to use integration by parts.The trick for this is to correctly set 'u' and 'dv'. 'u' should be labelled as the function ...

Factorising is a way of simplifying an equation by putting it into common parts. In the equation above we can see that x is common to both the 5x^2 and the 20x. If we divide by x and put this in-front of ...

First, notice that any equation crosses the x-axis when y = 0.Second, notice that x² + x - 2 = 0 is an example of a quadratic equation. So, we generally do 1 of 3 things (Factorise, Complete th...

To prove (x+2) is a factor, the value of x that makes x+2 equal 0 must be substituted into the function g(x) also making g(x)=0. In this case, the value of x being -2 makes x+2 equal to 0 and when substit...