What is the integral of p^4ln(p) ?

The integral of p^4ln(p) is 1/5 p^5ln(p)-(p^5)/(25)+C

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integral of p^4ln(p)

\int p^{4} ln (p) d p

\frac{1}{5} p^{5} ln (p) - \frac{p ^{5}}{25} + C

Solution steps

\int p^{4} ln (p) d p

Apply Integration By Parts

: \frac{1}{5} p^{5} ln (p) - \int \frac{p ^{4}}{5} d p

= \frac{1}{5} p^{5} ln (p) - \int \frac{p ^{4}}{5} d p

\int \frac{p ^{4}}{5} d p = \frac{p ^{5}}{25}

= \frac{1}{5} p^{5} ln (p) - \frac{p ^{5}}{25}

Add a constant to the solution

= \frac{1}{5} p^{5} ln (p) - \frac{p ^{5}}{25} + C

3 \frac{d x}{d t} - 6 x = sin (2 t), x (0) = 1

\frac{d}{d x} (\frac{x}{y})

1 - sin^{2} (x)

\int \frac{13 x e ^{2 x}}{( 1 + 2 x ) ^{2}} d x

\frac{\partial}{\partial x} (3 sin (x))

What is the integral of p^4ln(p) ?
The integral of p^4ln(p) is 1/5 p^5ln(p)-(p^5)/(25)+C