\(\displaystyle \textrm{say that}\,\,\, u=(5+3x) \,\,\,\textrm{and}\,\,\, u'=\frac{d(3x)}{dx} \therefore\)

\(\displaystyle \int 3(5+3x)^6dx=\int u^6u'dx\)

\(\displaystyle \textrm{ This is were I get lost. It says that the answer to this would be}\,\,\,\frac{u^7}{7}+C\)

\(\displaystyle \textrm{But u' is a scalar so:} \,\,\, \int u^6u'dx=u'\int u^6dx\)

\(\displaystyle \textrm{and thus}\,\,\,\frac{d(3x)}{dx}\frac{u^7}{7}=3\frac{u^7}{7}\)

\(\displaystyle \textrm{So why does this book say}\,\, \frac{u^7}{7}\,\, \textrm{and not:} \,\, 3\frac{u^7}{7}\)

\(\displaystyle \textrm{thanks in advance}\) (Bow)