What is the integral of 8xln(2x) ?

The integral of 8xln(2x) is 8(1/2 x^2ln(2x)-(x^2)/4)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 8xln(2x)

\int 8 x ln (2 x) d x

8 (\frac{1}{2} x^{2} ln (2 x) - \frac{x ^{2}}{4}) + C

Solution steps

\int 8 x ln (2 x) d x

Take the constant out:

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

= 8 \cdot \int x ln (2 x) d x

Apply Integration By Parts

= 8 (\frac{1}{2} x^{2} ln (2 x) - \int \frac{x}{2} d x)

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= 8 (\frac{1}{2} x^{2} ln (2 x) - \frac{x ^{2}}{4})

Add a constant to the solution

= 8 (\frac{1}{2} x^{2} ln (2 x) - \frac{x ^{2}}{4}) + C

What is the integral of 8xln(2x) ?
The integral of 8xln(2x) is 8(1/2 x^2ln(2x)-(x^2)/4)+C