arctan(x)^1/2的不定积分

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/10 08:33:39
arctan(x)^1/2的不定积分arctan(x)^1/2的不定积分arctan(x)^1/2的不定积分√x=u,dx=2udu=∫2arctanudu^2=2u^2arctanu-2∫u^2/(

arctan(x)^1/2的不定积分
arctan(x)^1/2的不定积分

arctan(x)^1/2的不定积分
√x=u,dx=2udu
=∫2arctanudu^2
=2u^2arctanu-2∫u^2/(1+u^2)*du
=2u^2arctanu-2∫(u^2+1-1)/(1+u^2)*du
=2u^2arctanu-2u+2arctanu+C
=2xarctan√x-2√x+2arctan√x+C