What is the integral of 2ln(x)x^4 ?

The integral of 2ln(x)x^4 is 2(1/5 x^5ln(x)-(x^5)/(25))+C

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integral of 2ln(x)x^4

\int 2 ln (x) x^{4} d x

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

Solution steps

\int 2 ln (x) x^{4} d x

Take the constant out:

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

= 2 \cdot \int ln (x) x^{4} d x

Apply Integration By Parts

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

= 2 (\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}

= 2 (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25})

Add a constant to the solution

= 2 (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}) + C

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What is the integral of 2ln(x)x^4 ?
The integral of 2ln(x)x^4 is 2(1/5 x^5ln(x)-(x^5)/(25))+C