dx/(x^2*(ax+b)^0.5)的不定积分,要详解'我设(ax+b)^0.5=u没做出来'请...dx/(x^2*(ax+b)^0.5)的不定积分,要详解'我设(ax+b)^0.5=u没做出来'请大侠指导那个是根号下啊'晕死答案不对

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/14 17:58:00
dx/(x^2*(ax+b)^0.5)的不定积分,要详解'我设(ax+b)^0.5=u没做出来'请...dx/(x^2*(ax+b)^0.5)的不定积分,要详解'我设(ax+b)^0.5=u没做出来'请大侠指导那个是根号下啊'晕死答案不对

dx/(x^2*(ax+b)^0.5)的不定积分,要详解'我设(ax+b)^0.5=u没做出来'请...dx/(x^2*(ax+b)^0.5)的不定积分,要详解'我设(ax+b)^0.5=u没做出来'请大侠指导那个是根号下啊'晕死答案不对
dx/(x^2*(ax+b)^0.5)的不定积分,要详解'我设(ax+b)^0.5=u没做出来'请...
dx/(x^2*(ax+b)^0.5)的不定积分,要详解'我设(ax+b)^0.5=u没做出来'请大侠指导
那个是根号下啊'晕死答案不对

dx/(x^2*(ax+b)^0.5)的不定积分,要详解'我设(ax+b)^0.5=u没做出来'请...dx/(x^2*(ax+b)^0.5)的不定积分,要详解'我设(ax+b)^0.5=u没做出来'请大侠指导那个是根号下啊'晕死答案不对
∫dx/x^2√(ax+b)
=(-1/√b)∫d(1/x)/∫√(ax/b+1)
=(-a/b√b)∫d(b/ax)/√(ax/b+1)
b/ax=tanu^2
=(-a/b√b)∫2tanusecu^2 du/sinu
=(-2a/b√b)∫secu^3du
=(-a/b√b)[secutanu+ln|secu+tanu|
=(-a/b√b)[√(b/ax)+1) *(b/ax)+ln|√[(b/ax)+1] +(b/ax)|+C
∫secx^3dx=∫secxdtanx=secxtanx-∫tanx^2secxdx=secxtanx-∫(secx)^3dx+∫secxdx
2∫secx^3dx=secxtanx+∫secxdx=secxtanx+ln|secx+tanx|