What is the integral of x^{12}ln(x) ?

The integral of x^{12}ln(x) is 1/13 x^{13}ln(x)-(x^{13})/(169)+C

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integral of x^{12}ln(x)

\int x^{12} ln (x) d x

\frac{1}{13} x^{13} ln (x) - \frac{x ^{13}}{169} + C

Solution steps

\int x^{12} ln (x) d x

Apply Integration By Parts

: \frac{1}{13} x^{13} ln (x) - \int \frac{x ^{12}}{13} d x

= \frac{1}{13} x^{13} ln (x) - \int \frac{x ^{12}}{13} d x

\int \frac{x ^{12}}{13} d x = \frac{x ^{13}}{169}

= \frac{1}{13} x^{13} ln (x) - \frac{x ^{13}}{169}

Add a constant to the solution

= \frac{1}{13} x^{13} ln (x) - \frac{x ^{13}}{169} + C

\frac{d ^{2} y}{d t ^{2}} + 3 \frac{d y}{d t} + 2 y = 0

\int (2 + tan (x))^{2} d x

f (x) = 4 sec^{2} (x)

f (x) = 5 x 1 - x^{3}

\frac{d}{d x} (\frac{7 x + 8}{4 x + 8})

What is the integral of x^{12}ln(x) ?
The integral of x^{12}ln(x) is 1/13 x^{13}ln(x)-(x^{13})/(169)+C