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 ▸A ball is released from rest at a height of 4m. At what speed does it hit the ground?
Differentiate with respect to x, x^2*e^(tan(x))
∫ x^3 *ln(2x) (from 2->1) can be written in the form pln 2 + q, where p and q are rational numbers. Find p and q.
find dy/dx of the equation y=ln(x)2x^2