解答题
28.求∫arctan(1＋
【正确答案】令
＝t，则
∫arctan(1＋
)dχ＝∫arctan(1＋t)d(t2)＝t2arctan(1＋t)－
＝t2arctan(1＋t)－
＝t2arctan(1＋t)－t＋ln(t2＋2t＋2)＋C
＝χarctan(1＋
)－
＋ln(χ＋2
＝t，则∫arctan(1＋
)dχ＝∫arctan(1＋t)d(t2)＝t2arctan(1＋t)－＝t2arctan(1＋t)－
＝t2arctan(1＋t)－t＋ln(t2＋2t＋2)＋C
＝χarctan(1＋
)－＋ln(χ＋2【答案解析】