What is the integral of log_{b}(x) ?

The integral of log_{b}(x) is xlog_{b}(x)-x/(ln(b))+C

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integral of log_{b}(x)

\int lo g_{b} (x) d x

x lo g_{b} (x) - \frac{x}{ln ( b )} + C

Solution steps

\int lo g_{b} (x) d x

Apply Integration By Parts

: x lo g_{b} (x) - \int \frac{1}{ln ( b )} d x

= x lo g_{b} (x) - \int \frac{1}{ln ( b )} d x

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

= x lo g_{b} (x) - \frac{x}{ln ( b )}

Add a constant to the solution

= x lo g_{b} (x) - \frac{x}{ln ( b )} + C

y + x = 4, 36 - 9 x = y^{2}

\frac{d}{d t} (A \cdot (cos (ω t + φ)))

y^{^{'}} (x) = \frac{x ^{2}}{1 - y ^{2}}, y (4) = 2

\int 2 x e^{x} d x

y = (x^{2} + 1)^{3}

What is the integral of log_{b}(x) ?
The integral of log_{b}(x) is xlog_{b}(x)-x/(ln(b))+C