What is the integral of 2xln(3x) ?

The integral of 2xln(3x) is x^2ln(3x)-(x^2)/2+C

Popular >

integral of 2xln(3x)

\int 2 x ln (3 x) d x

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

Solution steps

\int 2 x ln (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 ln (3 x) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} ln (3 x) - \int \frac{x}{2} d x

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

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

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

Simplify

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

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

Add a constant to the solution

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

n = 1 \sum \infty 2 π^{- n}

x \to \infty lim (\frac{3 ^{3 \cdot x}}{3 ^{x}})

\frac{x ^{5}}{5 - x ^{4}}

\frac{d ^{3}}{d x ^{3}} (x^{3})

\frac{\partial}{\partial x} (x^{0.5} + y^{0.5})

What is the integral of 2xln(3x) ?
The integral of 2xln(3x) is x^2ln(3x)-(x^2)/2+C