高数题求详细解答如图谢谢

运用极坐标代换
xrcosa,yrsina,a[0,2π],r[0,1],dxdyrdrda
∫∫ln(1+x＾2+y＾2)dσ
∫[0,2π]∫[0,1]ln(1+r^专2)rdrda
∫[0,2π]da∫[0,1]ln(1+r^2)rdr
π∫属[0,1]ln(1+r^2)d(1+r^2)
令1+r^2z
π∫[1,2]lnzdz
πzlnz[1,2]-πz[1,2]
2πln2-π