Complete the indefinite integral : ∫x lnx dx
Use the formula: ∫uv' dx = uv - ∫u'v dx (use I = the integral we're looking for)Note we cant integrate ln x easily but we can differentiate into 1/x so we use:u = ln x and v' = x we have u' = 1/x and v = x2/2 subbing these values into the above formula we get:I = x2/2 lnx - ∫1/x x2/2 dx = x2/2 lnx - ∫x/2 dx= x2/2 lnx - x2/4 + C
KD
Related Maths A Level answers
All answers ▸How do I differentiate (cosx)/x^2
A stone, of mass m , falls vertically downwards under gravity through still water. The initial speed of the stone is u . Find an expression for v at time t .
A particle of mass 0.5 kg is moving down a rough slope (with coefficient of friction = 0.2) inclined at 30 degrees to the horizontal. Find the acceleration of the particle. Use g = 9.8 ms^-2.
Integrate 3x^4-4x^2+3/x