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use the substitution u=2+ln(x) to show that int(e,1(ln(x)/x(2+ln(x)^2))dx)=p+ln(q) , where p and q are rational numbers.

So u=2+lnx, therefore du/dx=1/x , we can work out the new upper and new lower limit by substitute in e and 1 into 2+lnx , and we get 2+ln(e)=3 , 2+ln(1)=2Rearrange the differential we get dx=xdu , substitute...
Answered by • Maths tutor
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Solve the quadratic inequality: x^2 - 5x + 4 < 0

x 2 -5x+4 &lt;0First we ignore the inequality and try to solve the equation x 2 -5x+4=0, which we do via factorising (x-4)(x-1)=0. x = 4 or x=1We draw the graph using our solution, going through the points o...
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Answered by Hariz H. • Maths tutor
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Solve the following simultaneous equations to find x and y.

2x 2 - 2y = 282y - 4 = 12x y - 2 = 6xy = 6x + 2 Substitute y = 6x + 2 2x 2 - 2(6x + 2) = 282x 2 - 12x - 4 = 282(x 2 - 6x - 2) = 28x 2 - 6x - 2 = 14x 2 - 6x - 16 = 0(x - 8)(x + 2) = 0 if x = 8 then y = 50if x...
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Answered by Prahlad D. • Maths tutor
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What is the electron figuration of a copper ion? The n what is the electron configuration of a copper2+ ion

The electron configuration is:{Ar]4s13d10Copper donates one of the electrons in its S orbital to the d orbital in order to make itself more stableCopper 2+ is [Ar]3d9The 4s electrons are lost first as they a...
Answered by • Chemistry tutor
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Explain the formation of a wave cut platform.

A wave cut platform is formed when softer rock at sea level is eroded by the processes of hydraulic action and abrasion. These processes erode the rock to create a notch in the rock, which is eroded further ...
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Answered by Alice M. • Geography tutor
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