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

The integral of 6xln(2x) is 6(1/2 x^2ln(2x)-(x^2)/4)+C

Popular >

integral of 6xln(2x)

\int 6 x ln (2 x) d x

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

Solution steps

\int 6 x ln (2 x) d x

Take the constant out:

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

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\int_{0}^{2 π} x e^{- i x} d x

\int x \cdot cos (x) - x \cdot sin (x) d x

\int 3 x^{2} ln (x) d x

x \to 0 lim (- 2 g (x))

\frac{\partial}{\partial x} (x^{2} + x)

What is the integral of 6xln(2x) ?
The integral of 6xln(2x) is 6(1/2 x^2ln(2x)-(x^2)/4)+C