What is the integral of $ln (3 x)$ $ln(3x)$ ?

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Answer 1 · 2015-04-13T19:20:21

$x ln (3 x) - x + C$ $xln(3x)-x+C$

Detailed Solution

$\int ln (3 x) d x$ $intln(3x)dx$

$= \int 1 . ln (3 x) d x$ $=int1.ln(3x)dx$

Integrating by parts

$= ln (3 x) . (x) - \int \frac{1}{3 x} . (3) . (x) d x$ $=ln(3x).(x)-int1/(3x).(3).(x)dx$

$=xln(3x)-intcancel(3x)/cancel(3x)dx$

$=xln(3x)-intdx$

$=xln(3x)-x+C$

What is the integral of ln(3x)ln(3x)ln(3x)?