What is the integral of p^5ln(p) ?

The integral of p^5ln(p) is 1/6 p^6ln(p)-(p^6)/(36)+C

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integral of p^5ln(p)

\int p^{5} ln (p) d p

\frac{1}{6} p^{6} ln (p) - \frac{p ^{6}}{36} + C

Solution steps

\int p^{5} ln (p) d p

Apply Integration By Parts

: \frac{1}{6} p^{6} ln (p) - \int \frac{p ^{5}}{6} d p

= \frac{1}{6} p^{6} ln (p) - \int \frac{p ^{5}}{6} d p

\int \frac{p ^{5}}{6} d p = \frac{p ^{6}}{36}

= \frac{1}{6} p^{6} ln (p) - \frac{p ^{6}}{36}

Add a constant to the solution

= \frac{1}{6} p^{6} ln (p) - \frac{p ^{6}}{36} + C

\frac{d y}{d x} = \frac{x y + 2}{x + 1}

\frac{d}{d t} (t - cos (t))

x \to + 2 lim (x 13 - x^{2})

\int 1 + \frac{2}{x} d x

\frac{d}{d x} (cos (sin (5 x^{2})))

What is the integral of p^5ln(p) ?
The integral of p^5ln(p) is 1/6 p^6ln(p)-(p^6)/(36)+C