what is the integration of ㏒ltenxl ?
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Strategy: Use Integration by Parts.ln(x) dxset
u = ln(x), dv = dx
then we find
du = (1/x) dx, v = xsubstitute ln(x) dx = u dvand use integration by parts= uv - v dusubstitute u=ln(x), v=x, and du=(1/x)dx= ln(x) x - x (1/x) dx
= ln(x) x - dx
= ln(x) x - x + C
= x ln(x) - x + C.
Q.E.D.
u = ln(x), dv = dx
then we find
du = (1/x) dx, v = xsubstitute ln(x) dx = u dvand use integration by parts= uv - v dusubstitute u=ln(x), v=x, and du=(1/x)dx= ln(x) x - x (1/x) dx
= ln(x) x - dx
= ln(x) x - x + C
= x ln(x) - x + C.
Q.E.D.
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