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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...

Solution: x=4. This can be shown by factorisation or applying the quadratic formula.

Pythagoras theorem works to find out an unknown side length of a right angles triangle (RAT) knowing the other two lengths. A RAT has 3 sides called a hypotenuse (longest side), and two smaller sides. We ...