What is the integral of x^{100}ln(x) ?

The integral of x^{100}ln(x) is 1/101 x^{101}ln(x)-(x^{101})/(10201)+C

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integral of x^{100}ln(x)

\int x^{100} ln (x) d x

\frac{1}{101} x^{101} ln (x) - \frac{x ^{101}}{10201} + C

Solution steps

\int x^{100} ln (x) d x

Apply Integration By Parts

: \frac{1}{101} x^{101} ln (x) - \int \frac{x ^{100}}{101} d x

= \frac{1}{101} x^{101} ln (x) - \int \frac{x ^{100}}{101} d x

\int \frac{x ^{100}}{101} d x = \frac{x ^{101}}{10201}

= \frac{1}{101} x^{101} ln (x) - \frac{x ^{101}}{10201}

Add a constant to the solution

= \frac{1}{101} x^{101} ln (x) - \frac{x ^{101}}{10201} + C

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What is the integral of x^{100}ln(x) ?
The integral of x^{100}ln(x) is 1/101 x^{101}ln(x)-(x^{101})/(10201)+C