What is the integral of 2x+4xln(8x) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 2x+4xln(8x)

\int 2 x + 4 x ln (8 x) d x

2 x^{2} ln (8 x) + C

Solution steps

\int 2 x + 4 x ln (8 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 x d x + \int 4 x ln (8 x) d x

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

\int 4 x ln (8 x) d x = 2 x^{2} ln (8 x) - x^{2}

= x^{2} + 2 x^{2} ln (8 x) - x^{2}

Simplify

= 2 x^{2} ln (8 x)

Add a constant to the solution

= 2 x^{2} ln (8 x) + C

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