What is the integral of x^{1000}ln(x) ?

The integral of x^{1000}ln(x) is 1/1001 x^{1001}ln(x)-(x^{1001})/(1002001)+C

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integral of x^{1000}ln(x)

\int x^{1000} ln (x) d x

\frac{1}{1001} x^{1001} ln (x) - \frac{x ^{1001}}{1002001} + C

Solution steps

\int x^{1000} ln (x) d x

Apply Integration By Parts

: \frac{1}{1001} x^{1001} ln (x) - \int \frac{x ^{1000}}{1001} d x

= \frac{1}{1001} x^{1001} ln (x) - \int \frac{x ^{1000}}{1001} d x

\int \frac{x ^{1000}}{1001} d x = \frac{x ^{1001}}{1002001}

= \frac{1}{1001} x^{1001} ln (x) - \frac{x ^{1001}}{1002001}

Add a constant to the solution

= \frac{1}{1001} x^{1001} ln (x) - \frac{x ^{1001}}{1002001} + C

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What is the integral of x^{1000}ln(x) ?
The integral of x^{1000}ln(x) is 1/1001 x^{1001}ln(x)-(x^{1001})/(1002001)+C