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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.

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 a...

Using the chain rule, Let y=cos²(x)Let u=cos(x)y=u²dy/du=2udu/dx=-sin(x)dy/dx=dy/du*du/dx=-2sin(x)cos(x)

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 equati...

Consider two scenarios before and after. Before there is a velocity of 8m/s (with right being positive) and mass 1kg. after there is a mass of 1kg and a velocity of -4 m/s as right is positive and it boun...