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How do you integrate ln(x) with respect to x?

This integral must be done using integration by parts. Therefore, we set u=ln(x) and dv=dx, which gives du=1/x and v=x. Then, using the integration by parts formula the integral now equals x*ln(x)-int[dx]. T...
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Answered by Oliver H. • Maths tutor
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The equation 2x^2 + 2kx + (k + 2) = 0, where k is a constant, has two distinct real roots. Show that k satisfies k^2 – 2k – 4 > 0

Two distinct real roots means that we can use b^2-4ac>0 relationship for any ax^2+bx+c equation. Apply the above gives, 4k^2 - 4 2 (k+2)>0 Simplifying gives, k^2 - 2k -4 >0
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Answered by Andreas T. • Maths tutor
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How does the mechanism for electrophilic addition work?

First we must consider what an elecrophile is. An electrophile is a molecule or ion which is attracted to (and accepts electrons from) electron dense regions in other molecules, because it is positively char...
AR
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How to find and classify stationary points (maximum point, minimum point or turning points) of curve.

To find the stationary points of a function we must first differentiate the function. The derivative tells us what the gradient of the function is at a given point along the curve. Therefore, should we find ...
CJ
Answered by Callum J. • Maths tutor
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Find the equation of the tangent to the curve y = (2x -3)^3 at the point (1, - 1), giving your answer in the form y = mx + c.

y = (2x -3)^3 y = (2x)^3 + 3.((2x)^2)(-3) + 3.(2x).(-3)^2 + (-3)^2 using Pascal's Triangle. y = 8x^3 - 36x^2 + 54x - 27 dy/dx = 24x^2 - 72x + 54 at point (1,-1); dy/dx = 24 -72 + 54 = 6 Therefore tangent lin...
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Answered by Robert S. • Maths tutor
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