求不定积分∫rln(1+r²)dr,

分类: 作业答案 • 2021-12-31 20:40:03

问题描述：

求不定积分∫rln(1+r²)dr,

答

∫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)