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Euclid's algorithm is really useful to be able to, firstly, see if two numbers are co-prime, in other words to see if they share any common factors, but also to find solutions to equations. Say we have tw...

(x+2)(x-3)(x+4)^2 = (x^2 - x - 6)(x^2 + 8x + 16) = (x^4 + 8x^3 +16x^2 - x^3 - 8x^2 -16x - 6x^2 - 48x - 96) 

= x^4 +7x^3 + 2x^2 - 64x - 96)

When integrating, you need to add one to the power and divide the term by the power. We will consider each term individually, 2x⁴ will become (2x⁴⁺¹)/(4+1) = (2x⁵)/5, -4x<...

As f '(x) is the differential of f(x) we have to first integrate f '(x). To do this we take each term individually and integrate it. So starting with 3x², to integrate a simple function of x li...