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Using integration by parts split it into v'=(1/x^3) and u=ln(x). v=-1/2x^2 and u'=1/x. Integral ln(x)/(x^3) = u*v - Integral u'*v = -ln(x)*1/2x^2 - 1/4x^2 + c

In order to integrate the expression we must first rewrite it in terms of Partial Fractions i.e. A/x and B/(2-x), so that when multiplied together we have a fraction with same denominator as the expressio...

Due to notation difficulties, S = integral sign. This is a straightforward integration question, firstly we expand the brackets:

f'(x)=3x^2 - 3x f(x)=S(3x^2 - 3x)dx f(x)=3/3x^3 - 3/2x^2 + C f(x)=x^...

y-(any value of the function)=0.5(x-(any value in the domain))

e.g. Point with point A being (1,14) The answer would be y-14=0.5(x-1)

cos(x) + (1/2)sin(x) :

Rsin(x + a) = R{sin(x)cos(a) + cos(x)sin(a)} = (1/2)sin(x) + (1)cos(x) (comparing coeffs.)

Therefore Rcos(a) = 1/2 and separately Rsin(a) = 1 So tan(a) = 2 and R^2 =...