What is the integral of p^3ln(p) ?

The integral of p^3ln(p) is 1/4 p^4ln(p)-(p^4)/(16)+C

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integral of p^3ln(p)

\int p^{3} ln (p) d p

\frac{1}{4} p^{4} ln (p) - \frac{p ^{4}}{16} + C

Solution steps

\int p^{3} ln (p) d p

Apply Integration By Parts

: \frac{1}{4} p^{4} ln (p) - \int \frac{p ^{3}}{4} d p

= \frac{1}{4} p^{4} ln (p) - \int \frac{p ^{3}}{4} d p

\int \frac{p ^{3}}{4} d p = \frac{p ^{4}}{16}

= \frac{1}{4} p^{4} ln (p) - \frac{p ^{4}}{16}

Add a constant to the solution

= \frac{1}{4} p^{4} ln (p) - \frac{p ^{4}}{16} + C

y = x^{4}, y = x^{2}

x \to 4 - lim (\frac{4 x}{x - 4})

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

\int_{2}^{4} (x^{2} + 2)^{3} d x

y^{^{''}} + y = t, y (0) = 1, y (1) = - 2

What is the integral of p^3ln(p) ?
The integral of p^3ln(p) is 1/4 p^4ln(p)-(p^4)/(16)+C