What is the integral of x^8*ln(x) ?

The integral of x^8*ln(x) is 1/9 x^9ln(x)-(x^9)/(81)+C

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integral of x^8*ln(x)

integral

x^{8} \cdot ln (x)

\frac{1}{9} x^{9} ln (x) - \frac{x ^{9}}{81} + C

Solution steps

\int x^{8} ln (x) d x

Apply Integration By Parts

= \frac{1}{9} x^{9} ln (x) - \int \frac{x ^{8}}{9} d x

\int \frac{x ^{8}}{9} d x = \frac{x ^{9}}{81}

= \frac{1}{9} x^{9} ln (x) - \frac{x ^{9}}{81}

Add a constant to the solution

= \frac{1}{9} x^{9} ln (x) - \frac{x ^{9}}{81} + C

in t e g r a l \frac{x}{( 1 + x ) ^{2}}

in t e g r a l \frac{1}{e ^{- x}}

in t e g r a l \frac{1}{sec ( x )}

in t e g r a l \frac{1}{( x ^{2} - x )}

in t e g r a l \frac{( 2 x + 1 )}{( x ^{2} + 1 )}

What is the integral of x^8*ln(x) ?
The integral of x^8*ln(x) is 1/9 x^9ln(x)-(x^9)/(81)+C