Question

Integrate sqrt(x)lnxdx

Answer 1

\[\int\limits \sqrt{x}\ln(x)dx\]

I'm going to assume that's the correct integral, above. You're going to use parts, which takes the form: \[\int\limits udv = uv - \int\limits vdu\]
u = ln(x) dv = √x
\[du = \frac{ 1 }{ x }\] \[v = \frac{ 2 }{ 3 } x^{\frac{ 3 }{ 2 }}\]

Answer 2

\[\frac{ 2 }{ 9 }x^{\frac{ 3 }{ 2 }}(3\ln(x)-2)+C\]