What is the integral of (ln(x))/(x^{2021)} ?

The integral of (ln(x))/(x^{2021)} is -(ln(x))/(2020x^{2020)}-1/(4080400x^{2020)}+C

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integral of (ln(x))/(x^{2021)}

\int \frac{ln ( x )}{x ^{2021}} d x

- \frac{ln ( x )}{2020 x ^{2020}} - \frac{1}{4080400 x ^{2020}} + C

Solution steps

\int \frac{ln ( x )}{x ^{2021}} d x

Apply Integration By Parts

: - \frac{ln ( x )}{2020 x ^{2020}} - \int - \frac{1}{2020 x ^{2021}} d x

= - \frac{ln ( x )}{2020 x ^{2020}} - \int - \frac{1}{2020 x ^{2021}} d x

\int - \frac{1}{2020 x ^{2021}} d x = \frac{1}{4080400 x ^{2020}}

= - \frac{ln ( x )}{2020 x ^{2020}} - \frac{1}{4080400 x ^{2020}}

Add a constant to the solution

= - \frac{ln ( x )}{2020 x ^{2020}} - \frac{1}{4080400 x ^{2020}} + C

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What is the integral of (ln(x))/(x^{2021)} ?
The integral of (ln(x))/(x^{2021)} is -(ln(x))/(2020x^{2020)}-1/(4080400x^{2020)}+C