What is the integral of (ln(x))/(81) ?

The integral of (ln(x))/(81) is 1/81 (xln(x)-x)+C

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integral of (ln(x))/(81)

\int \frac{ln ( x )}{81} d x

\frac{1}{81} (x ln (x) - x) + C

Solution steps

\int \frac{ln ( x )}{81} d x

Take the constant out:

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

= \frac{1}{81} \cdot \int ln (x) d x

Apply Integration By Parts

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

= \frac{1}{81} (x ln (x) - \int 1 d x)

\int 1 d x = x

= \frac{1}{81} (x ln (x) - x)

Add a constant to the solution

= \frac{1}{81} (x ln (x) - x) + C

\int x^{3} e^{- 2 x^{2}} d x

x y^{^{'}} + y = 2 e^{2 x}

f (x) = x^{9}

\int 8 tan^{2} (x) + tan^{4} (x) d x

y^{2} = 4 x + 4, y = 4 x + 16

What is the integral of (ln(x))/(81) ?
The integral of (ln(x))/(81) is 1/81 (xln(x)-x)+C