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Firstly we look at the term 2(x^3). The power of x (in this case 3) is multiplied by the factor of x (in this case 2) and the power is then reduced by 1. This means it is 2x3(x^{3-1}) which simplifies to ...

Firstly we divide up the equations into its three compenents based on the powers of the x values, giving us 3x^2, 2x^(1/2) and -12. Now one at a time, we multiply the coefficient by the power of x, and th...

The first step to answering this question is to get the equation in a simpler form. Aim to have it solely in terms of sin(x) and cos(x) with no fractional parts.                                           ...

We must use the factor theorem since that is what the question asks. So we take p(x) and think about the factors of 8 we then evaluate it at x=1 to start, then move onto x=-1,2,-2 and so on. We see that i...

The general formula for integration by parts is given as
∫u(dv/dx)dx = uv - ∫v(du/dx)dx
given that the equation to be solved is ∫x²sin2xdx, the values for u, v, du/dx and dv/dx can ...