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

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

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integral of (x^5ln(x))

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\int_{0}^{1} \frac{2}{x ( 1 + x )} d x

f (x) = arcsin (x)

\frac{2}{4 s ^{2} - 8 s}

\int_{2}^{4} \frac{( 2 x - 3 ) x}{6} d x

x \to - 2 lim (- x^{2} + 6 x - 1)

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