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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 + ...

The key thing to remember with fractions, is that adding and subtracting them require a COMMON DENOMINATOR. We achieve this by multiplying both the top and bottom of fractions by a number that allows us t...

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...

These are simultaneous equations. To solve them, we need to do something to these equations to that either the coefficents of x or y are the same. So multiply each equation by a suitable number,  a good c...