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

The integral of 3xln(2x) is 3(1/2 x^2ln(2x)-(x^2)/4)+C

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integral of 3xln(2x)

\int 3 x ln (2 x) d x

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

Solution steps

\int 3 x ln (2 x) d x

Take the constant out:

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

= 3 \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

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

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

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

Add a constant to the solution

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

y = x (6 x + 1)^{5}

x \to i lim (x^{2} + 2 x)

\int_{0}^{t a n (x)} \frac{1}{1 + t ^{2}} d t

\frac{x ^{2} - x - 2}{x ^{2} - 6 x + 9}

\frac{d}{d x} (arctan (5^{x}))

What is the integral of 3xln(2x) ?
The integral of 3xln(2x) is 3(1/2 x^2ln(2x)-(x^2)/4)+C