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Intergrating with respect to time, you get that v = u + at. Knowing that velocity is just the rate of change of your position ds/dt = v, and sustituting the previous expression for v, you get ds/dt = u + ...

We begin by quoting the integration by parts formula, as the question speciaficaly asks us to use it.

integrate(u(x) v'(x) dx)|^(b)(a) = [u(x) v(x)]^(b)(a) - integrate(u'(x) v(x) dx)|^(b)_...

The question states to use integration by parts. So first we recall the integration by parts formula is integrate(u(x)v'(x)  dx)=     (v(x)u(x))    -    integrate(u'(x)v(x)   dx)+c...

Firstly, Integrate the f'(x) equation by raising the power by 1 and then dividing by the new power and adding a constant c. This gives you f(x)=(12x^3)/3 -(8x^2)/2 + x + c Then you simplify, f(x)=4x^3 -4x...

Tackle differentiation questions in two parts: First put it into the simplest for possible for differenciation, then perform the differenciation. 

So for this equation you should first expand the t...