What is the integral of x^4ln(9x) ?

The integral of x^4ln(9x) is 1/5 x^5ln(9x)-(x^5)/(25)+C

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integral of x^4ln(9x)

\int x^{4} ln (9 x) d x

\frac{1}{5} x^{5} ln (9 x) - \frac{x ^{5}}{25} + C

Solution steps

\int x^{4} ln (9 x) d x

Apply Integration By Parts

: \frac{1}{5} x^{5} ln (9 x) - \int \frac{x ^{4}}{5} d x

= \frac{1}{5} x^{5} ln (9 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 (9 x) - \frac{x ^{5}}{25}

Add a constant to the solution

= \frac{1}{5} x^{5} ln (9 x) - \frac{x ^{5}}{25} + C

y^{^{''}} + 4 y^{^{'}} - 3 y = x

\frac{d}{d x} (sin^{2} (x) + cos^{2} (x))

\int e^{- \frac{t}{2}} d t

y^{^{''}} = 8 t^{2}

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

What is the integral of x^4ln(9x) ?
The integral of x^4ln(9x) is 1/5 x^5ln(9x)-(x^5)/(25)+C