What is the integral of xlog_{3}(x^2) ?

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

\int x lo g_{3} (x^{2}) d x

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

Solution steps

\int x lo g_{3} (x^{2}) d x

Simplify

lo g_{3} (x^{2}) : 2 lo g_{3} (x)

= \int 2 x lo g_{3} (x) d x

Take the constant out:

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

= 2 \cdot \int x lo g_{3} (x) d x

Apply Integration By Parts

= 2 (\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 )}

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

Simplify

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

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

Add a constant to the solution

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

\int 6 x^{3} e^{- 5 x} d x

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

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

\int \frac{2 cos ( x )}{x ^{3}} d x

\int sec^{4} (x) cos^{3} (x) d x

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