Evaluate the Integral: $\int \frac{\log_{10}\ x}{x}\ dx$ $\int \frac{\log_{10}\ x}{x}\ dx$
$du=x\ln10\ dx$
$\log_{10}x\  \ln10+ C$
Is this answer correct? If not what step should I take to convert the log into a term I can manipulate?  

$$\int { \frac { \log _{ 10 }{ x }  }{ x } dx } =\int { \log _{ 10 }{ x } d\ln { x } =\log _{ 10 }{ x } \ln { x } -\int { \frac { \ln { x }  }{ x\ln { 10 }  } +C= }  } \\ =\log _{ 10 }{ x } \ln { x } -\frac { 1 }{ \ln { 10 }  } \int { \ln { x } d\ln { x } +C= } \log _{ 10 }{ x } \ln { x } -\frac { 1 }{ \ln { 10 }  } \ln { x } +C=\\ =\ln { x\left( \log _{ 10 }{ x } -\frac { 1 }{ \ln { 10 }  }  \right) +C } $$
