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Integrate ln(x) wrt dx

Integrate by parts. First rewrite the integral in the form u dv/dx, which is (1)ln(x). Then integrate (1)ln(x) wrt dx by assigning u=ln(x) du/dx=1/x and dv/dx=1 v=x. We can determine the integral of ln(x), u...
ST
Answered by Sathurthini T. • Maths tutor
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Express x^2 - 7x + 2 in the form (x - p)^2 + q , where p and q are rational numbers.

This is an example of completing the square.If we expand (x - p)^2 + q, we will have x^2 -2px + p + q.Now we can use algebra to work out what p and q are from the following equation. x^2 - 7x + 2 = x^2 -2px ...
CP
Answered by Catherine P. • Maths tutor
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Given a fixed parabola and a family of parallel lines with given fixed gradient, find the one line that intersects the parabola in one single point

Let the parabola be y=x 2 and let the family of lines be y=2x+c, in order to study the intersection points we need to consider the second order linear system given by having the two equations above. Hence, w...
FT
Answered by Francesca T. • Maths tutor
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Find all solution to the equation 3tan(x)=8/sin(x) for 0<=x<=360 degrees

By multipying across and using some trigonometric identities we can turn this in to a much simpler quatratic which can be solved using the quadratic formula. This step can be simplified by using the substitu...
JB
Answered by James B. • Maths tutor
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Differentiate with respect to x: F(x)=(x^2+1)^2

To differentiate composite functions, (a function within a function) like in this case we need to use the chain rule. We can see that F(x)=f(g(x)) where we let f(x)= (x^2+1)^2 and g(x)= x^2+1. To use the cha...
LG
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