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

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

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integral of x^4ln(4x)

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

\frac{1}{5} x^{5} ln (4 x) - \frac{x ^{5}}{25} + C

Solution steps

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

Apply Integration By Parts

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

= \frac{1}{5} x^{5} ln (4 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 (4 x) - \frac{x ^{5}}{25}

Add a constant to the solution

= \frac{1}{5} x^{5} ln (4 x) - \frac{x ^{5}}{25} + C

x \to - 6 - lim (\frac{1}{( x + 6 ) ^{4}})

n = 0 \sum \infty ln (\frac{n + 1}{n})

y^{^{''}} + y = sin (2 t)

x \to 5 lim (- 2 x)

f (x) = 3 x + \frac{2}{x}

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