What is the integral of 14xln(2x) ?

The integral of 14xln(2x) is 14(1/2 x^2ln(2x)-(x^2)/4)+C

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integral of 14xln(2x)

\int 14 x ln (2 x) d x

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

Solution steps

\int 14 x ln (2 x) d x

Take the constant out:

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

= 14 \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

= 14 (\frac{1}{2} x^{2} ln (2 x) - \int \frac{x}{2} d x)

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

= 14 (\frac{1}{2} x^{2} ln (2 x) - \frac{x ^{2}}{4})

Add a constant to the solution

= 14 (\frac{1}{2} x^{2} ln (2 x) - \frac{x ^{2}}{4}) + C

\frac{d}{d x} (cos^{2} (3 x^{7}))

\frac{\partial}{\partial x} (x^{\frac{1}{4}} y^{\frac{1}{4}})

\int \frac{5 ^{x}}{ln ( 5 )} d x

x \to \infty lim (20)

y = \frac{1}{x ^{2}}, (- 2, \frac{1}{4})

What is the integral of 14xln(2x) ?
The integral of 14xln(2x) is 14(1/2 x^2ln(2x)-(x^2)/4)+C