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For integration by parts, the integral is uv - ∫ u' v dx. First we take u = ln x and v' = 1. While we could have u and v' be the opposite at this stage, it becomes apparent later on that we can't do this ...

Question:Particle P of mass m and particle Q of mass km are moving in opposite directions on a smooth horizontal plane when they collide directly. Immediately before the collision the spe...

3x²-(1/4)x^-2+3
Split the problem into three separate terms and integrate independently.With any term where x is to the power of something, divide the coefficient by the value of...

The first thing to notice here is that the denominator of the integrand is a case of 'difference of two squares'. The integral, which I will call I, can be rewritten as the integral of 4/((1+x)(1-x)) dx. ...

Firstly we remind ourselves of the integration by parts formula. The formula used to integrate u dv/dx with respect to x = uv - the integral of v du/dx with respect to x.
So the first thing we have t...