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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of log_{a}(x)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

\frac{d x}{d t} = t x - 2 x + t - 2

x \to 0 lim (\frac{1 - cot ( x )}{\frac{1}{x}})

\int 6 x^{5} d x

\frac{d}{d x} (\frac{7 x ^{2}}{4 e ^{x} - x})

\frac{\partial}{\partial y} (e^{x y z^{3}} y z^{3})

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