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

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

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integral of (x^4ln(x))

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\frac{d}{d x} (50 x - 5 x)

\int \frac{x ^{2} + 1}{( x - 10 ) ( x - 9 ) ^{2}} d x

(x^{2} + 81) (\frac{d y}{d x}) = 2, y (9) = 0

(x + 2)^{2} + (y - 3)^{2} = 37, (4, 2)

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