急!! 求∫(1 to 2) (z^5*lnz) dz!!?

Key: ∫ uv' = uv - ∫ u'v


∫(1 to 2) (z^5*lnz) dz u = ln(z) du = 1/z
v' = z^5 v = 1/6 * z^6

= (z^6 * lnz)/6 + ∫ (1/z)*(1/6 * z^6) dz

= [ (z^6 * lnz)/6 + (z^6)/36 ] (1 to 2)

= ( 32 ln (2) )/3 - 7/4