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

The integral of (ln(x))/3 is 1/3 (xln(x)-x)+C

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integral of (ln(x))/3

\int \frac{ln ( x )}{3} d x

\frac{1}{3} (x ln (x) - x) + C

Solution steps

\int \frac{ln ( x )}{3} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int ln (x) d x

Apply Integration By Parts

: x ln (x) - \int 1 d x

= \frac{1}{3} (x ln (x) - \int 1 d x)

\int 1 d x = x

= \frac{1}{3} (x ln (x) - x)

Add a constant to the solution

= \frac{1}{3} (x ln (x) - x) + C

\int cos^{2} (x) tan (x) d x

\int \frac{sin ( x ) - x}{x} d x

\int \frac{1 - x ^{2} - 3 x ^{2}}{x ^{\frac{2}{3}}} d x

\int (\frac{1}{( x ^{2} - 1 )}) d x

\int (sec^{2} (x) (1 + tan (x))) d x

What is the integral of (ln(x))/3 ?
The integral of (ln(x))/3 is 1/3 (xln(x)-x)+C