What is the integral of x^5ln(3x) ?

The integral of x^5ln(3x) is 1/6 x^6ln(3x)-(x^6)/(36)+C

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integral of x^5ln(3x)

\int x^{5} ln (3 x) d x

\frac{1}{6} x^{6} ln (3 x) - \frac{x ^{6}}{36} + C

Solution steps

\int x^{5} ln (3 x) d x

Apply Integration By Parts

: \frac{1}{6} x^{6} ln (3 x) - \int \frac{x ^{5}}{6} d x

= \frac{1}{6} x^{6} ln (3 x) - \int \frac{x ^{5}}{6} d x

\int \frac{x ^{5}}{6} d x = \frac{x ^{6}}{36}

= \frac{1}{6} x^{6} ln (3 x) - \frac{x ^{6}}{36}

Add a constant to the solution

= \frac{1}{6} x^{6} ln (3 x) - \frac{x ^{6}}{36} + C

\int 12 x^{2} - 10 x + 4 d x

\frac{d}{d x} (\frac{π}{2 x ^{5}})

\int 3 x^{2} + 4 d x

x \to 3 lim (x^{2} + 7 + 5)

y = 4 x^{3} 1 - x^{2}

What is the integral of x^5ln(3x) ?
The integral of x^5ln(3x) is 1/6 x^6ln(3x)-(x^6)/(36)+C