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∫ (ln(x)/(x*(1+ln(x))^2) dx

use u = 1+ln(x) as the substitution du/dx = 1/xdx = x du ∫ (ln(x)/(x*(1+ln(x))^2) dx = ∫ ((u-1) x/ x (u^2)) du = ∫ (u-1)/(u^2) du
JB
Answered by Jack B. • Maths tutor
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A circle C has centre (-5, 12) and passes through the point (0,0) Find the second point where the line y=x intersects the circle.

The equation of a circle comes in a standard format of (x-a) 2 + (y-b) 2 = r 2 where (a, b) are the coordinates of the centre of the circle and r is the radiusFrom the information, we can find the radius of ...
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Differentiate Sin^2(X) with respect to X

'With respect to X' means we will be differentiating all the X parts (To put it simply). First we show that the differential of Sin(X) is Cos(X), we can show this graphically using the whiteboard. Then we sh...
TH
Answered by Thomas H. • Maths tutor
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A particle, P, moves along the x-axis. The displacement, x metres, of P is given by 0.5t^2(t^2 - 2t + 1), when is P instantaneously at rest

differenciate and then eqate with v = 0.
HS
Answered by Harry S. • Maths tutor
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f(x) = sinx. Using differentiation from first principles find the exact value of f' (π/6).

The derivative of the function where x=π/6 is defined asThe limit as h->0 of [sin(h+π/6)-sin(π/6)]/hUsing the double angle formula, sin(h+π/6) = sin(h)cos(π/6) + cos(h)sin(π/6) = √3sin(h)/2 + cos(h)sin(π/...
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