What is the integral of x^{77}ln(x) ?

The integral of x^{77}ln(x) is 1/78 x^{78}ln(x)-(x^{78})/(6084)+C

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integral of x^{77}ln(x)

\int x^{77} ln (x) d x

\frac{1}{78} x^{78} ln (x) - \frac{x ^{78}}{6084} + C

Solution steps

\int x^{77} ln (x) d x

Apply Integration By Parts

: \frac{1}{78} x^{78} ln (x) - \int \frac{x ^{77}}{78} d x

= \frac{1}{78} x^{78} ln (x) - \int \frac{x ^{77}}{78} d x

\int \frac{x ^{77}}{78} d x = \frac{x ^{78}}{6084}

= \frac{1}{78} x^{78} ln (x) - \frac{x ^{78}}{6084}

Add a constant to the solution

= \frac{1}{78} x^{78} ln (x) - \frac{x ^{78}}{6084} + C

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y = - x^{2} + 12 x - 32, y = 0

What is the integral of x^{77}ln(x) ?
The integral of x^{77}ln(x) is 1/78 x^{78}ln(x)-(x^{78})/(6084)+C