What is the integral of (x+4)ln(x) ?

The integral of (x+4)ln(x) is ln(x)((x^2)/2+4x)-1/2 ((x^2)/2+8x)+C

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integral of (x+4)ln(x)

\int (x + 4) ln (x) d x

ln (x) (\frac{x ^{2}}{2} + 4 x) - \frac{1}{2} (\frac{x ^{2}}{2} + 8 x) + C

Solution steps

\int (x + 4) ln (x) d x

Apply Integration By Parts

: ln (x) (\frac{x ^{2}}{2} + 4 x) - \int \frac{1}{2} (x + 8) d x

= ln (x) (\frac{x ^{2}}{2} + 4 x) - \int \frac{1}{2} (x + 8) d x

\int \frac{1}{2} (x + 8) d x = \frac{1}{2} (\frac{x ^{2}}{2} + 8 x)

= ln (x) (\frac{x ^{2}}{2} + 4 x) - \frac{1}{2} (\frac{x ^{2}}{2} + 8 x)

Add a constant to the solution

= ln (x) (\frac{x ^{2}}{2} + 4 x) - \frac{1}{2} (\frac{x ^{2}}{2} + 8 x) + C

n = 1 \sum \infty 6 (0.9)^{n - 1}

\int - 4 cos (x) - x d x

\frac{d}{d x} ((5 x^{3} - 3 x + 4)^{20})

y^{^{'}} = 7 y^{5}

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

What is the integral of (x+4)ln(x) ?
The integral of (x+4)ln(x) is ln(x)((x^2)/2+4x)-1/2 ((x^2)/2+8x)+C