高数求微积分紧急求大虾们第二部到第三部怎么计算得到.求给出稍微详细点的解题步骤

令 (1-r/R)^(1/n) = t,则 1-r/R = t^n,r=R(1-t^n),dr=-nRt^(n-1)dt
于是 [2πu/(πR^2)]∫(1-r/R)^(1/n)rdr
= (2u/R^2)∫ t[-nRt^(n-1)]R(1-t^n)dt
= (2nu)∫t^n(1-t^n)dt
= (2nu)∫[t^n-t^(2n)]dt
= (2nu)[t^(n+1)/(n+1)-t(2n+1)/(2n+1)]
= 2nu*n/[(n+1)(2n+1)]
= 2n^2u/[(n+1)(2n=1)]。