What is the integral of 14xln(5x) ?

The integral of 14xln(5x) is 14(1/2 x^2ln(5x)-(x^2)/4)+C

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integral of 14xln(5x)

\int 14 x ln (5 x) d x

14 (\frac{1}{2} x^{2} ln (5 x) - \frac{x ^{2}}{4}) + C

Solution steps

\int 14 x ln (5 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 (5 x) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} ln (5 x) - \int \frac{x}{2} d x

= 14 (\frac{1}{2} x^{2} ln (5 x) - \int \frac{x}{2} d x)

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

= 14 (\frac{1}{2} x^{2} ln (5 x) - \frac{x ^{2}}{4})

Add a constant to the solution

= 14 (\frac{1}{2} x^{2} ln (5 x) - \frac{x ^{2}}{4}) + C

\frac{\partial}{\partial x} (4 x^{3} y^{2} - 2)

y = x^{4} - 2 x^{3} - 9

\int (x - 1) d x

x \to 0 lim (\frac{x}{1 - x})

\frac{\partial}{\partial x} (sin (x - 3 y))

What is the integral of 14xln(5x) ?
The integral of 14xln(5x) is 14(1/2 x^2ln(5x)-(x^2)/4)+C