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Integrate ln(x)/(x^3)

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
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Answered by Archie A. • Maths tutor
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Find the integral of (x+4)/x(2-x) .dx

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 expression w...
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Answered by Aaron T. • Maths tutor
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If f'(x)=3x(x - 1), find f(x)

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^3 - 3/2x^2...
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Answered by Grace R. • Maths tutor
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The point A lies on the curve y=5(x^2)+9x , The tangent to the curve at A is parralel to the line 2y-x=3. Find an equation to this tangent at A.

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)
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Answered by Rehman A. • Maths tutor
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Express cos(x) + (1/2)sin(x) in terms of a single resultant sinusoidal wave of the form Rsin(x+a)

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 = 5/4. Answer: sqrt(...
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Answered by Hakkihan T. • Maths tutor
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