What is the integral of 3xln(x) ?

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

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integral of 3xln(x)

\int 3 x ln (x) d x

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

Solution steps

\int 3 x ln (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 (x) d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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

1 0^{x}

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

\int_{0}^{1} (x^{10} + 1 0^{x}) d x

y^{'} - \frac{2}{t} y = t^{2} e^{t}

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