What is the integral of (x+9)ln(x) ?

The integral of (x+9)ln(x) is ln(x)((x^2)/2+9x)-1/2 ((x^2)/2+18x)+C

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integral of (x+9)ln(x)

\int (x + 9) ln (x) d x

ln (x) (\frac{x ^{2}}{2} + 9 x) - \frac{1}{2} (\frac{x ^{2}}{2} + 18 x) + C

Solution steps

\int (x + 9) ln (x) d x

Apply Integration By Parts

: ln (x) (\frac{x ^{2}}{2} + 9 x) - \int \frac{1}{2} (x + 18) d x

= ln (x) (\frac{x ^{2}}{2} + 9 x) - \int \frac{1}{2} (x + 18) d x

\int \frac{1}{2} (x + 18) d x = \frac{1}{2} (\frac{x ^{2}}{2} + 18 x)

= ln (x) (\frac{x ^{2}}{2} + 9 x) - \frac{1}{2} (\frac{x ^{2}}{2} + 18 x)

Add a constant to the solution

= ln (x) (\frac{x ^{2}}{2} + 9 x) - \frac{1}{2} (\frac{x ^{2}}{2} + 18 x) + C

\frac{1}{x ^{2} + 1}, 0

\frac{d}{d x} (\frac{x ^{7}}{7} + \frac{2 x}{3})

f (x) = (2 x - 5)^{4} (x^{2} + x + 1)^{5}

\int (t^{2} + 2 t + 1)^{4} d t

25 y^{^{''}} + 3 y = 0

What is the integral of (x+9)ln(x) ?
The integral of (x+9)ln(x) is ln(x)((x^2)/2+9x)-1/2 ((x^2)/2+18x)+C