求不定积分∫rln(1+r²)dr,

来源：学生作业帮助网编辑：作业帮时间：2024/11/16 20:43:51

求不定积分∫rln(1+r²)dr,
求不定积分∫rln(1+r²)dr,

求不定积分∫rln(1+r²)dr,
∫rln(1+r2)dr
=(1/2)∫ln(1+r2)d(1+r2)
=(1/2)[(1+r2)ln(1+r2)-∫(1+r2)dln(1+r2)]
=(1/2)[(1+r2)ln(1+r2)-∫1dr]
=(1/2)(1+r2)ln(1+r2)-(r/2)