How can you integrate ln(x) with respect to x?
We can use substitution for this one. Take y=ln(x) to be equal to y= 1 x ln(x)Set u=ln(x) and dv/dx=1Compute du/dx and v:du/dx=1/x and v=xUse given formula - ∫ udv/dx dx = uv - ∫ vdu/dx dx= xln(x) - ∫ x/x dx= xln(x) - x (+C)This is the complete proof, however this is an easy one to remember and may be useful to memorise.
SH
Related Maths A Level answers
All answers ▸Describe the set of transformations that will transformthe curve y=x^ to the curve y=x^2 + 4x - 1
integrate cos(2x) + sin(3x)
A small stone is projected verically upwards from a point O with a speed of 19.6ms^-1. Modeeling the stone as a particle moving freely under gravity find the time for which the stone is more than 14.6m above O
Find the equation of the tangent at x=1 for the curve y=(4x^2+1)^3