What is the integral of 5x^4ln(x) ?

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

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integral of 5x^4ln(x)

\int 5 x^{4} ln (x) d x

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

Solution steps

\int 5 x^{4} ln (x) d x

Take the constant out:

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

= 5 \cdot \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

= 5 (\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}

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

Simplify

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

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

Add a constant to the solution

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

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