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

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

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integral of x^4ln(5x)

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

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

Solution steps

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

Apply Integration By Parts

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

\int \frac{x ^{4}}{5} d x = \frac{x ^{5}}{25}

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

Add a constant to the solution

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

(ln (x^{3}))^{^{'}}

in v erse l a pl a ce \frac{1}{( s - 1 ) ( s ^{2} - 1 )}

\int \frac{( x ^{3} + 64 )}{x ^{2} + 64} d x

\int_{0}^{7} 1

d er i v a t i v e (x (x^{2} + 4))^{\frac{1}{3}}

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