What is the integral of 9xln(x) ?

The integral of 9xln(x) is 9(1/2 x^2ln(x)-(x^2)/4)+C

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integral of 9xln(x)

\int 9 x ln (x) d x

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

Solution steps

\int 9 x ln (x) d x

Take the constant out:

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

= 9 \cdot \int x ln (x) d x

Apply Integration By Parts

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

= 9 (\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x)

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

= 9 (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4})

Add a constant to the solution

= 9 (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}) + C

x \to - 2 lim (4^{x} cos (π x))

e^{3 x^{3}}

y = x (x - 8)

2^{3 x + 1}

\frac{d}{d r} (\frac{r}{r ^{2} + 1})

What is the integral of 9xln(x) ?
The integral of 9xln(x) is 9(1/2 x^2ln(x)-(x^2)/4)+C