What is the integral of (x+2)ln(x) ?

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

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integral of (x+2)ln(x)

\int (x + 2) ln (x) d x

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

Solution steps

\int (x + 2) ln (x) d x

Apply Integration By Parts

: ln (x) (\frac{x ^{2}}{2} + 2 x) - \int \frac{1}{2} (x + 4) d x

= ln (x) (\frac{x ^{2}}{2} + 2 x) - \int \frac{1}{2} (x + 4) d x

\int \frac{1}{2} (x + 4) d x = \frac{1}{2} (\frac{x ^{2}}{2} + 4 x)

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

Add a constant to the solution

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

x = 9, x = y^{2}

\int \frac{6}{t ^{2}} d t

\int 12 x + 12 d x

\int \frac{e ^{4 x} + 4 e ^{x} + 8}{e ^{x}} d x

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

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