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

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

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integral of 5xln(5x)

\int 5 x ln (5 x) d x

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

Solution steps

\int 5 x ln (5 x) d x

Take the constant out:

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

= 5 \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

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

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

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

Add a constant to the solution

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

\int \frac{1}{2 x ^{2}} d x

y = (7 t - 4), (0, 0.5)

\frac{d}{d x} (x^{t a n (x)})

\int_{1}^{9} \frac{2}{x} d x

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

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