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This question may start by giving you an equation, which you need to write in the form of the standard equation of a circle (usually by completing the square). This allows you to see the centre of the circle...

A: x 3 /3 + 3ln(x) + A. Step-by-step solution: Integral (x 2 +3/x dx) = [as integrals preserve sums] integral (x 2 dx) + integral (3/x dx) = [raise exponent by one, multiply by the reciprocal, add a constant...

If we apply a function and then its inverse, we should get back to where we started. Suppose we start with an element x. If we apply f to it, we get to x+2. In order to get back to where we started (i.e. x),...

This is often overlooked as no-one gives a reason to why this is and is often stated as a fact. We start off with the basic indice law of x y * x z = x y+z . For example, Likewise with division, you can have...

Trigonometric identities are sometimes tricky, as they are very hard to distinguish one from another. The best way of doing it is obviously by practising, but one thing I always find helpful is to give an ex...