What is the integral of 2xln(6x) ?

The integral of 2xln(6x) is x^2ln(6x)-(x^2)/2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2xln(6x)

\int 2 x ln (6 x) d x

x^{2} ln (6 x) - \frac{x ^{2}}{2} + C

Solution steps

\int 2 x ln (6 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 ln (6 x) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} ln (6 x) - \int \frac{x}{2} d x

= 2 (\frac{1}{2} x^{2} ln (6 x) - \int \frac{x}{2} d x)

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

= 2 (\frac{1}{2} x^{2} ln (6 x) - \frac{x ^{2}}{4})

Simplify

2 (\frac{1}{2} x^{2} ln (6 x) - \frac{x ^{2}}{4}) : x^{2} ln (6 x) - \frac{x ^{2}}{2}

= x^{2} ln (6 x) - \frac{x ^{2}}{2}

Add a constant to the solution

= x^{2} ln (6 x) - \frac{x ^{2}}{2} + C

\int sec (x) cot (x) d x

\int_{0}^{1} x^{4} - x d x

\int 1 - cos^{2} (θ) d θ

\frac{d}{d x} (7 x + 2)

y^{^{'}} + y = e^{- t} ln (t)

What is the integral of 2xln(6x) ?
The integral of 2xln(6x) is x^2ln(6x)-(x^2)/2+C