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How do you integrate ln(x) ?

-First write the integral with ln(x) and form a product of 1 next to it-Let u=ln(x) and differentiate this-Let dv/dx= 1 and integrate this-Substitute values into integration by parts formula-Simplify and add...
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Find the first derivative of f(x). f(x) = ln(3x^2+2x+1)

The differential of a natural log function gives a fraction where the numerator is the first derivative of what we are taking the natural log of and the denominator is what we are taking the natural log of. ...
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A curve C has equation y = x^2 − 2x − 24 x^(1/2), x > 0 (a) Find (i) dy/d x (ii) d^2y/dx^2 (b) Verify that C has a stationary point when x = 4 (c) Determine the nature of this stationary point, giving a reason for your answer.

(a) i) dy/dx= 2x-2-12x -1/2 ii) d 2 y/dx 2 = 2+6x -3/2 (b) Substitute x=4 into dy/dx= 2x-2-12x -1/2 Show that dy/dx= 0 and state 'hence there is a stationary point' (c) Substitute x=4 into d 2 y/dx 2 = 2+6x ...
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f ( x ) = 2 x ^3 − 5 x ^2 + ax + a. Given that (x + 2) is a factor of f ( x ), find the value of the constant a. (3 marker)

If x+2 is definitely a factor, that means when we sub x=-2 in, we should get 0 at the end. So 2(-2)^3 - 5(-2)^2 + a(-2) + a = 0So -16 -20= aso a = -36
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Express 4x/(x^2-9) - 2/(x+3) as a single fraction in its simplest form.

In order to add or subtract terms to/from each other, both of their denominators (the number on the bottom of the fraction) must be the same. In this case they are different, so the first step is to try and ...
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