What is the integral of xlog_{3}(x) ?

The integral of xlog_{3}(x) is 1/2 x^2log_{3}(x)-(x^2)/(4ln(3))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of xlog_{3}(x)

\int x lo g_{3} (x) d x

\frac{1}{2} x^{2} lo g_{3} (x) - \frac{x ^{2}}{4 ln ( 3 )} + C

Solution steps

\int x lo g_{3} (x) d x

Apply Integration By Parts

= \frac{1}{2} x^{2} lo g_{3} (x) - \int \frac{x}{2 ln ( 3 )} d x

\int \frac{x}{2 ln ( 3 )} d x = \frac{x ^{2}}{4 ln ( 3 )}

= \frac{1}{2} x^{2} lo g_{3} (x) - \frac{x ^{2}}{4 ln ( 3 )}

Add a constant to the solution

= \frac{1}{2} x^{2} lo g_{3} (x) - \frac{x ^{2}}{4 ln ( 3 )} + C

What is the integral of xlog_{3}(x) ?
The integral of xlog_{3}(x) is 1/2 x^2log_{3}(x)-(x^2)/(4ln(3))+C