What is the integral of p^2ln(p) ?

The integral of p^2ln(p) is 1/3 p^3ln(p)-(p^3)/9+C

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integral of p^2ln(p)

\int p^{2} ln (p) d p

\frac{1}{3} p^{3} ln (p) - \frac{p ^{3}}{9} + C

Solution steps

\int p^{2} ln (p) d p

Apply Integration By Parts

: \frac{1}{3} p^{3} ln (p) - \int \frac{p ^{2}}{3} d p

= \frac{1}{3} p^{3} ln (p) - \int \frac{p ^{2}}{3} d p

\int \frac{p ^{2}}{3} d p = \frac{p ^{3}}{9}

= \frac{1}{3} p^{3} ln (p) - \frac{p ^{3}}{9}

Add a constant to the solution

= \frac{1}{3} p^{3} ln (p) - \frac{p ^{3}}{9} + C

x \to 0 lim (x^{2} - 2 x)

\int \frac{x - 1}{( x ^{2} + 2 x + 3 ) ^{2}} d x

f (x) = \frac{1}{x}, at x = 0.501

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

What is the integral of p^2ln(p) ?
The integral of p^2ln(p) is 1/3 p^3ln(p)-(p^3)/9+C