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

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

\int 3 x (x^{2} + 8)^{2} d x

\int x^{2} (x^{3} + 8)^{10} d x

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

\int \frac{1}{x ( x ^{6} + 1 )} d x

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