Question

Integration:

Answer 1

\[\LARGE \int ln~\sqrt[3]{x}~dx\]

Answer 2

take it by part, let u = ln (cuberoot x) dv =dx

Answer 3

Is my derivative right for u?
\(\LARGE u=ln \sqrt[3]{x}\) and \(\LARGE dv=dx\)

\(\LARGE du=\frac{1}{\sqrt[3]{x}}~dx\) and \(\LARGE v=x\)

\(\LARGE (ln\sqrt[3]{x})x~-~ \int (x)(\frac{1}{\sqrt[3]{x}})~dx\)

^Evaluate that?

Answer 4

nope, for u
du = 1/(3x) , you forgot chain rule