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Integrate ln(x)

Take ln(x) = 1 * ln(x) and integrate by parts. Let u = ln(x) and dv/dx = 1 such that du/dx = 1/x and v = x. Using the integrating by parts formula, you get x ln(x) - integral(1) = x ln(x) - x + c.
JY
Answered by Jason Y. • Maths tutor
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A ball of mass m moves towards a ball of mass km with speed u. The coefficient of restitution is 0. What is the final velocity if the first ball after the collision.

Coefficient of restitution is defined as the ratio of the relative speed of separation of the balls to the relative speed of approach. A ratio of 0 means that the speed of separation has a value of zero as t...
SE
Answered by Susannah E. • Maths tutor
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Differentiate cos^2(x)

Using the chain rule, Let y=cos 2 (x)Let u=cos(x)y=u 2 dy/du=2udu/dx=-sin(x)dy/dx=dy/du*du/dx= -2sin(x)cos(x)
MB
Answered by Manish B. • Maths tutor
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Find the equation of the tangent to the curve x^3+yx^2=1 at the point (1,0).

We can find the gradient of a tangent to a curve at a point by finding dy/dx at x=1.Firstly we can rearrange the equation of the curve for y.(1) yx^2=1-x^3(2)y=x^{-2}-xThen we can differentiate the equation ...
OG
Answered by Ollie G. • Maths tutor
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Explain the mechanism by which DNA is replicated

DNA is replicated by semi-conservative replication meaning that each double stranded DNA molecule replicates to form two new double stranded molecules - each with one original and one new strand. This occurs...
GC
Answered by Georgie C. • Biology tutor
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