What is the integral of 2x^8ln(x) ?

The integral of 2x^8ln(x) is 2(1/9 x^9ln(x)-(x^9)/(81))+C

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integral of 2x^8ln(x)

\int 2 x^{8} ln (x) d x

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

Solution steps

\int 2 x^{8} ln (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \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

= 2 (\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}

= 2 (\frac{1}{9} x^{9} ln (x) - \frac{x ^{9}}{81})

Add a constant to the solution

= 2 (\frac{1}{9} x^{9} ln (x) - \frac{x ^{9}}{81}) + C

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What is the integral of 2x^8ln(x) ?
The integral of 2x^8ln(x) is 2(1/9 x^9ln(x)-(x^9)/(81))+C