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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)-i...

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 - 42(k+2)>0 Simplifying gives, k^2 - 2k -4 >0

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 c...

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 ...

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 -7...