Question 363520
Integrate by parts,
{{{int(u,dv)=uv-int(v,du)}}}
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{{{u=ln(x)}}}, {{{dv=dx/sqrt(x)}}}
{{{du=dx/x}}}, {{{v=2sqrt(x)}}}
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Substituting,
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{{{int(ln(x)/sqrt(x),dx)=2*ln(x)*sqrt(x)-int((2sqrt(x))/x),dx)}}}
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{{{int(ln(x)/sqrt(x),dx)=2*ln(x)*sqrt(x)-int(2/sqrt(x)),dx)}}}
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{{{int(ln(x)/sqrt(x),dx)=2*ln(x)*sqrt(x)-4*sqrt(x)+C}}}
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{{{highlight(int(ln(x)/sqrt(x),dx)=2*sqrt(x)(ln(x)-2)+C)}}}