∫根号下ln²(1-x)dx
来源:学生作业帮助网 编辑:作业帮 时间:2024/10/10 05:25:29
∫ln(1-√x)dx=xln(1-√x)+(1/2)∫√x/(1-√x)dx=xln(1-√x)-(1/2)∫(1-√x-1)/(1-√x)dx=xln(1-√x)-(1/2)x+(1/2)∫1/(
原式=∫1/√(1-ln²x)*1/xdx=∫1/√(1-ln²x)dlnx=arcsin(lnx)+C
∫dx/[x√(4-ln²x)]=∫dlnx/√(4-ln²x)=∫dt/√(4-t²)=∫d(t/2)/√[1-(t/2)²]=∫dm/√(1-m²
∫ln(x+√(1+x^2))dx=xln(x+√(1+x^2)-∫xd(ln(x+√(1+x^2))=xln(x+√(1+x^2)-∫xdx/√(1+x^2)=xln(x+√(1+x^2)-(1/2
不对,用分部积分法可以算出来
∫ln(x+根号(x^2+1))dx=xln(x+√(x²+1))-∫xdln(x+√(x²+1))=xln(x+√(x²+1))-∫x/√(x²+1)dx=x
用分步积分法∫ln(x+1)/√xdx=2∫ln(x+1)d√x=2ln(x+1)*√x-2∫√xdln(x+1)=2ln(x+1)*√x-2∫√x/(x+1)dx对于∫√x/(x+1)dx令√x=t
∫ln(x+√(1+x^2))dx=xln(x+√(1+x^2)-∫xd(ln(x+√(1+x^2))[ln(x+√1+x^2)]'=[1+x/√(1+x^2)]/(x+√(1+x^2))=1/√(1
(sqrt(x+1)*((4*x+1)*log(sqrt(x+1)+sqrt(x))-log(sqrt(x+1)-sqrt(x))-2*x*log(x))+sqrt(x)*((4*x+1)*log(s
∫1/(x(ln√x)^3)dx=8∫1/(lnx)^3)dlnx=-4/(lnx)^2+C
用分步积分∫x*ln(x-1)dx=1/2∫xln(x-1)dx^2=1/2x^2ln(x-1)-1/2∫x^2dln(x-1)=1/2x^2ln(x-1)-1/2∫x^2/(x-1)dx=1/2x^
∫dx/x[根号1-(ln^2)x]=∫d(lnx)/[根号1-(ln^2)x]=∫dt/[根号1-t^2](设t=lnx)=arcsint+C=arcsin(lnx)+C
∫1/[x√(1-ln²x)]dx=∫1/√(1-ln²x)d(lnx)=arcsin(lnx)+C公式:∫dx/√(a²-x²)=arcsin(x/a)+C
f(x)={ln[x+√(1+x2)]}'=1/[x+√(1+x2)]*[1+2x/2√(1+x2)]=1/√(1+x2)∫xf'(x)dx=∫xdf(x)=xf(x)-∫f(x)dx=x/√(1+x
用分部积分法:∫x*ln(x-1)dx=1/2∫xln(x-1)dx^2=1/2x^2ln(x-1)-1/2∫x^2dln(x-1)=1/2x^2ln(x-1)-1/2∫x^2/(x-1)dx=1/2
或直接将1/√(1+x^2)dx凑成ln[x+√(1+x^2)]即可,满意请采纳,谢谢.
1/x是lnx的导数,所以1/xdx=d(lnx).∫ln(√x)/xdx=1/2×∫lnxdlnx=1/2×1/2×(lnx)^2+C
用分步积分法∫[-1,1]ln[x+√(1+x^2)]dx=xln[x+√(1+x^2)][-1,1]-∫[-1,1]xdln[x+√(1+x^2)]=ln(√2+1)-ln(√2-1)-∫[-1,1