What is the integral of x^{11}ln(x) ?

The integral of x^{11}ln(x) is 1/12 x^{12}ln(x)-(x^{12})/(144)+C

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integral of x^{11}ln(x)

\int x^{11} ln (x) d x

\frac{1}{12} x^{12} ln (x) - \frac{x ^{12}}{144} + C

Solution steps

\int x^{11} ln (x) d x

Apply Integration By Parts

: \frac{1}{12} x^{12} ln (x) - \int \frac{x ^{11}}{12} d x

= \frac{1}{12} x^{12} ln (x) - \int \frac{x ^{11}}{12} d x

\int \frac{x ^{11}}{12} d x = \frac{x ^{12}}{144}

= \frac{1}{12} x^{12} ln (x) - \frac{x ^{12}}{144}

Add a constant to the solution

= \frac{1}{12} x^{12} ln (x) - \frac{x ^{12}}{144} + C

\int \frac{sec ^{3} ( x )}{tan ^{2} ( x )} d x

\frac{\partial}{\partial x} (16 x + 32 y - 1600)

\frac{x}{x + 1}

n = 0 \sum \infty \frac{1}{n ^{3} - n}

\int \frac{1}{x ^{3} - 4 x ^{2} + 3 x} d x

What is the integral of x^{11}ln(x) ?
The integral of x^{11}ln(x) is 1/12 x^{12}ln(x)-(x^{12})/(144)+C